Everyone's recipe is different I bet.... Here is mine. I am usually numb to those things and I don't volunteer anything. People believe what they want to believe. The only place I draw the line is (and I can make this as clearly as needed): I don't tell you what to do so you don't get to tell me either

I will only get confrontational if they get confrontational. I never bring up the subject first. I'm old. They might kick my ass! ?

The only time I care is at work where I have to tolerate ignorant assholes as long as they're not abusive. IRL, I don't worry about offending anyone because they're for damn sure not worried about offending me.

Context, context, context.

Are we having a free-flowing, logic-driven, debate-style discussion in an academic setting? Or are we responding to unsolicited opinions overheard in the grocery store check-out line? Are we chewing the fat with friends? Or getting an earful from Auntie Martha?

I love me some debate. I am not afraid to disagree, to tell someone they're wrong--or to be wrong, to concede a point, or "lose" an argument. I am not fully attached to or identified with my ideas, attitudes, and beliefs--so if they get poked full of holes, I can merrily thank the guy with the drill--for helping me along in my intellectual development. Mental formations for me are toys--which I am happy to share, trade, modify, smash, or throw away, as called for. I don't get possessive over them.

I have found that most people are not like me in this regard. So great is the divergence and so thorough its distribution that I basically don't count on ever running across someone with similar attitudes. (It does happen--just so seldomly that I can't count on it.) I pretty much just figure that everyone is identified with their mental formations to such a degree that it won't be fun or enjoyable for me to engage with them on a level that's worth my time and effort. Too much potential for bruised egos; not enough enough likelihood of satisfying exchange. Too much con; not enough pro.

And that's just ideas in general. Multiply that by the factor of religious belief and faith--and now you're playing with plutonium.
I'm conflict-averse, so I avoid making people cranky at all costs. I realize this is less of an issue for others.

I've found that people (due to identification) don't always distinguish between criticism of an idea versus cricism of a person. You can be very clear and direct and explicitly say, "I'm not attacking you; I'm attacking this idea..." and they will still consider and feel and respond as if you've attacked them. And nothing you can say will break that identification. Try as you might to present yourself as fair, reasonable, and polite, there are times when you will be perceived as unreasonable, unfair, and rude--and there's nothing you can do about it, because it's not coming from you at all.

Are you being asked for your opinion directly? Are you feeling an urge to speak out in response to undirected assertions that are made in your presence? Are your positions being attacked? Are you being given unsolicited advice, or otherwise told what to do?

Basically, I keep my mouth shut as much as possible. I only engage people when a) the cost-benefit analysis indicates a net plus to my engagement, as in academic settings or among people whom I know to be mature and rational; b) I'm being backed into a corner by someone who's being inappropriately overbearing and I cannot opt out of saying something.

Maybe you're less conflict-averse than I. Maybe you feel more pressure to speak out when you hear things you don't like. All well and good. I'm not advocating for anyone to behave the way I do--rather just presenting they way I see and process things.

For me: no rudeness, ever. Kindness and manners always. Not only because I feel it's the right thing to do: nothing rankles your self-styled "enemies" more than when they lose composure and resort to immature, inappropriate behavior--and you don't.

I think there's a big difference between being rude and politely pointing out the truth. It's possible to criticize without being an asshole. If you're engaged in a discussion with someone and they are clearly spewing bullshit, I'd try to keep the high ground as much as I could and correct them politely. Once you sink to their level the discussion ceases to be productive. Hope this helps.

It's always tempting isn't it, and oh so easy, but really it's best to politely disagree and move on.

Use comedy

This is something I struggle with all the time, I am an impulsive smart ass when people refuse to reason. I have to suppress my instincts and continue to be nice to them so that even if we don't agree on one instance they might be willing to listen the next time.

I try to lead the conversation onto a point that we can both agree on and then leave it there.
I am never respectful of anyones delusions. I do try to maintain balance and and be respectful towards the person, which is often difficult to do. It does not matter how rude they are I try to remain dignified. If they want to make themselves into an ass it is usually because they know they are loosing the argument and want to bait you into saying something rude so they can ignore the topic and tell everyone how rude you are.

In this case I just say "This conversation is not going anywhere lets talk about something else."

Another tactic I use is to be personal. I say something like "When I was a Christian ____ made me question if the Bible was real." In this case, I am not attacking them or their beliefs. I am simply sharing my personal struggle with God with them. This is playing on sympathy, I will admit, but Its a great way to get a point across. Perhaps they have asked themselves the same question or now will later.

It depends. If the person is constantly preaching, I might let them know that I don't think it's an appropriate time or place. I will let them know I'm not interested in debating the issue with them at this time. I will let them know that I respect their right to believe what they want, and that I expect them to respect my rights as well. But, when the time is right, I have no shame in letting someone know that I think the beliefs they want to share with me are delusional at best, and that magic thinking doesn't work for me. If they want a real debate, I try to give them one, even knowing they aren't hearing me. Then I come on this site to reinforce my need to know that not everyone treasures blind faith.

It really depends what you want to achieve but you should always be polite and don't get on your high-horse or grandstand. Some people will enter into debate and then it can be quite fun to politely take on their misconceptions regarding things like Evolution by Natural Selection and to show that atheists are thinking, moral people too. Other folk who react aggressively or just stonewall you with stock "I'm right, you're wrong" rhetoric are a waste of time - just agree to disagree with them.

It has been my experience that when you start poking holes in peoples belief system their first reaction is going to be to call you an asshole. Personal I don't bring it up with most people until they start in.

I agree with @Wurlitzer; picking your battles is essential. Sometimes, you just have to politely tell people that you will agree to disagree, and see if you can change the topic. Other times, just walk away. Sometimes, they will still label you an asshole, just because you didn't bow to their worldview. But, that is a problem they will have to live with - not you.

Don't drink the poison offered by other people; they can keep it for themselves.

Criticism can and should be offered in a non-disrespectful way. If anyone accepts another's honest and legitimate criticism as disrespectful, that is their problem and should not prevent anyone from voicing their criticism.

I’d say you’ve got every right to buck against judgemental rudeness from religious people, but you’ve also gotta pick your battles. Speak up if you have a cohesive point to make but don’t talk logic til you’re blue in the face at people that value evidence very little and seem incapable of changing their mind. To the people who are completely set in their ways, it’s probably more valuable to make sure they see you taking the higher road than them. Not that this means not speaking out, but being compassionate in how you choose to do so is more valuable than being zealous. Zeal and fervor at the expense of civility is the realm of the religious.

You always have the right to be rude to anyone at any time whether they have been disrespectful to you or not. The consequences will probably be about the same in either case because they probably don’t think they’ve been disrespectful. So all you have to decide is whether you will be happy with the consequences of your actions.

I don't deal with it. We all have our beliefs, and I respect theirs even if they don't return the favor.

Live and let live if they treat you disrespectful chew their head off lol

There is no line in the sand. Something that offends one person may not offend another. The only way to avoid offending anyone is to avoid topics of religion and politics. Unless you know who you’re talking to and know that they won’t get offended. Front my experience, most people are overly sensitive when they are religious. Either because you’re talking to someone who is brand new to their faith and they don’t want you questioning their new found beliefs because they wouldn’t have changed their old beliefs unless they were “sure” that they were right. And older members don’t want you questioning them because they’ve devoted their lives to it and they cling onto their beliefs too tightly.

Thus, the best option is to avoid conversations that include religion. It’s one of those subjects that people don’t want to be questioned about because they are sure they are right.

One thing I always try to remember is that what someone believes is typically the most important thing to them. So if I am having the conversation with an individual, I make a point of making it clear that I respect that what they believe is important to them. I also make it clear that I am not attacking them personally, but rather a belief system which I hold to be false, harmful, and among the worst viruses to ever infect humanity. If they are rude or disrespectful I typically don't fire back, though I may say something along the lines of: "you just said more about yourself, than you did about me..."

I see most religious people as having inherited mental infirmity; most are programed from a young age. Patience is required in dealings with them, just as one does with a child IMO. I seek commonaility and stress the potential value and goodness of human beings, emphasize common human needs, and seek solely rational ways of solving human problems in any "discussion". Alternatives to dogma are rare and thought provoking for some I talk to who havn't lost the ability to reason. Others may fuck off....

You make your point, but avoid the ad hominems. Honestly sometimes you have to a little rough around the edges and bluntly tell people what’s on your mind and risk being offensive. The truth is offensive to us as egotistical creatures ( I know that from experience because I have a huge ego). You can usually (not always) tell if you’re stepping over line by the reaction of the people in the background. Are the people who you are not interacting with in the dialogue looking away from you or giving you puzzled looks? Do you see them shying away from the situation? If you are feeling abnormally upset by someone/a situation, calm down and ask yourself why you’re feeling this upset. As long as you remain calm and simply state your case I can gaurentee that you are not being a prick, despite what the other disagreeing party might say to the contrary. If you’re not the one making a scene then 9/10 times you are behaving in a socially acceptable manner.

As a final note, be aware of your ideological opponents situation. Would they benefit from your criticism? As an example would you be openly critical of someone’s faith who lost a loved one or is close to death themselves and their faith is helping them cope? I suspect that wouldn’t b the case due to both the sympathy and empathy you posses (same for me). So there are considerations for the audience you are addressing.

Overall, if you’re asking this question chances are you’re already doing a pretty good job of being a nice respectful person already because you are self aware enough of your actions and words to have others on your mind.

One can't. Not because being an outspoken atheist is automatically being an arsehole, but because ANY challenge to religious belief is automatically considered to be disrespectful. It's written into the manual, to the point where some faiths think you should be killed for your temerity.
Continuing the standard of polite conversation and reasonable argumentation (IE avoiding logical fallacies) is about the best that can be done. Once it descends to Ad Homs you're probably best served by pointing out their crap argumentation and walking away.

I speak up whenever I think its needed. "Speak your truth quietly and clearly. Listen to others, even the dull and ignorant. They too have their story." Being rude only says who you are, not that the comments you received are rude. Always be polite, but know when to stop and step away. (and sometimes stepping away can be rude).

If someone you’re around and engaging with brings out ‘the prick’ in you and you feel that they are disrespecting you - run away. Do not waste your time or energy on them. Thank them for their time. Wish them a good day and walk away.