It would only really bother me when these statements are followed by the word 'but'.
Anything said before the word 'but' can be disregarded...

Thank you so much for your responses! I'm going to go through them again and answer who I didn't answer. I really like both sides of the argument and can understand how this could be taken as rude or that the person is trying to show that they're not going to treat you horribly. I've come to open my mind a bit more regarding these responses. Thank you!

When I get that, I simply reply, “Right, and I accept that you’re a Christian.” That usually turns the tables and shuts them right up.

This just doesn't happen in England.

No one cares what you are.

I always say your acceptance is of no consequence to me.

Seems okay to me.
I agree it would be nice if they didn't feel you needed their acceptance and permission.
But better than making it clear they will pray for you to see the light and become religious.
Perhaps do the same to them. "You believe in a middle-eastern zombie? That is alright with me. I accept your weird cult beliefs, and won't criticize you for them."

I suppose you could respond by saying the same things back to them, "and I accept your beliefs too" or "your religion is ok with me".
Have some fun with it.

Don't think of it that way. It's more like they're worried that they'll offend you... It's like if you're gay, or transgender. They don't really know what to say about you.

So it's rude, but not deliberately so.

I get annoyed when they just go right into something like "Girl you just gotta trust God!" or "You know it's all part of God's plan, just pray and get into a good community!" And I'm always too taken aback by the assumption to actually say anything. I manage to get out something like "I appreciate your thoughts." And this usually happens at work so I can't say much because I find it a rude thing to talk about there.

I think I just take it to mean that they're aware that some Christians don't accept others' differing views, especially agnostic and atheistic views, and they're letting me know that they aren't going to berate me for having a different perspective.

I don't think it is rude if they have a good intention, it is like they assuring you that they won't judge you and it is safe to say so.

surveys show that nearly half the U.S. population think theism is required to be a moral person so atheism/agnosticism are stigmatized so I think it's people's awkward attempt to say they don't believe the immoral b.s.