Deal Breaker? Yes.

I believe a positive relationship should be based on mutual respect and honesty.

To assert faith (belief without evidence) is a methodology to determine truth (things that can be demonstrated with facts) is dishonest. Faith is the foundation of the religious mind-set. As I do not respect people who do not value truth over superstition, I do not engage with a theist on a social adventure.

It wouldn't really be a deal breaker for me. I think that what's really important are there rationality and morality. If they're moderate theists that are open minded and think things through rather than just believe what their priest/pastor tells them.
In this case, the only problem I foresee would be if we were to be raising kids as she will most likely want them raised in the church where I would rather raise them secularly as free thinkers. I would like to think I could work it out with the specific person in regards to the issue, but it very well might become a deal-breaker.
However, that's only in regards to child-rearing while a relationship would be based on who they are as a person.

It's less about them being religious and more about them not respecting that I'm not. I also have my own spiritual practices that will scare a lot of Christians, and expect that to be a deal breaker for them. Though, theoretically, if they were respectful and understanding I would have no issue dating them, the likelyhood of that makes my answer a yes.

Yes. I am very vocal about being atheist, I don't hide who I am. I am also center-left, politically; it means a lot to me, that the person that I choose to spend time with, also shares my values; anything else would just be lying to one another about who we really are, and I wouldn't be ok with that.

More so than it used to be, but it still depends on how religious they actually are.

If they're content to keep their religion to themselves and not try to convert others and provided they're going to be as tolerant of and willing to accept my atheism as I am regarding their religion, then no. One hint that I need to adopt their faith to be saved and I'm gone.

Not 100%. Maybe like 70% lol.

Key factors would be how they view others beliefs and what the requirement would be on that side. If they are live and let live, fine. If they are convert or die then nah.

It depends on a few things. Generally, no.

Yes

Does she put out or not? That's the dealbreaker.

Oh yeah

Most likely.

Only if they get so far gone that they cry about wanting to save an imaginary part of me so I can live in the sky with an imaginary god forever. Once they cry and argue this with you it is time to make tracks.