I'd tell them, and tell them why it was rude and/or offensive. What they choose to do with that information will tell a lot about them as a human.

"oops - excuse me, I thought you were someone I wanted to know "

If it was that offensive I would say "I can't believe you said that-its offensive-goodbye and walk away. If racist, anti LGBTQ, anti disabilities, anti diversity of any type I don't want that person in my life period.

I’d make a mental note of it and otherwise ignore it until a long term pattern emerged before making an assessment on whether to tolerate it, attempt an intervention, or disengage.

I find scathing sarcasm works wonders. It let's them know you know their game and are better at it ?

If they are comfortable enough saying this on the first meeting, they will say even more as time passes.

The question's too general - they could be being either funny or crass. Context would determine.

When a friend's father said something racist and offensive about Latinos, I replied:

"My daughter is half-Spanish," I said. "Claire is a hard worker. She recently won a full-ride scholarship from the University of Washington."

Still, I inwardly seethed for a year because I was too polite. I kept thinking I should have called him out on his racism.

Entirely depends on the situation... At times I turn the other cheek, at times I confront, at times I walk away.

"I refuse to be around an abusive drunk," I said, standing up. "I'm leaving now."

People are not perfect. Sometimes they make mistakes and say things out of context/character so not much. But it would depend on many things. If you are out to meet someone (1st date) it might be a signal to move on to someone else.

Say something like, "Sir, f we are going to be respectful of each other, we need to be honest. In that vein, I find your remark inappropriate for the following reasons . . . "

I would walk away - I am old enough to get away with wacky behaviour!

Smile and go away.

Do they know you enough to realize they said something you would find offensive? There is such a thing as being too sensitive, ya know? On the other hand, racist or other offensive crap will get them 3X rudeness back real quick!

I would just examine their behavior and see if they meant sincerely, jokingly, ironically. Context is very i think.

I'd first find out why they said it. Then if it wasn't justified, I'd drop them like a hot potato.

Depends on the circumstances, but I try not to bee too confrontational right out the gate. In a social setting with strangers, a woman was recommending a visit to a town nearby that was lovely, but warned that it was "really gay" and she saw two men holding hands. I just blurted out "well I LOVE the gays!" and then things got a little awkward. I just couldn't let that go.

There are degrees of both rudeness and offensiveness. My reaction would vary from a quiet chuckle to a punch in the face.

It depends if they meant it or not. Is it something they've not thought about? Have they been careless, or is it something they believe?

If they've tried to offend on purpose - call them out on it.

It would depend on circumstance and on whether it was a one-off or an ongoing habit.

If, for example, a howling lunatic burst in, yelling 'Donald Trump is the BEST PRESIDENT EVER!' then I could hardly complain if she said something rude.

Depends on what they said.

Sound them out to see where their boundaries are. Then offend and/or better yet shock them.
I have some lined up. My wife and I don't want children, she got pissed off with people asking why or saying she has plenty of time to change her mind, so I told her when this crops up to just tell people I was:
Firing blanks.
Limp as a soggy noodles
Worthless in my babymaker
Pleasurable but without purpose
Great company, a loving husband but despised by god who cursed my prick with worthlessness.

Literally told her to list all these at once and more. Really drive it home and do so even if im there. Especially if I'm there. In return when people bring that crap up with me I say:
She's a wonderful wife but not really a woman
She's a great lover but dry as a husk
Dead inside
Barren and soulless even
I love her but despite my efforts she will never contribute to humanity.
Again this goes on and on. I actually got to do it once. Was totally worth it. My wife loved hearing about it.

What is rude or offensive varies with the recipient. What you might find offensive could well bring raucous laughter from someone else. This is a question that is so subjective that no single answer would suffice.

I tell them it was rude and I keep talking.