You must be quite young because the answer was to never even get to that point., Be proud of yourself and amplify that with respectful ways that they are out too lunch and you do not want to go
In our younger years we continue to care about hurting other;s feelings and that is a wonderful training ground for reality, We know we are good, as to even care, but the only reason they keep trying is that they do believe you are the one lacking and they can indeed save you.
You are the one knowing and you may serve them a wonderful experience by saying bye bye

I'd say you were good.

However, I am perhaps them most outspoken atheist I know and, surrounded by theists, live alone with no expectations of every finding a suitable rational (not theist) woman to share my life with so my opinion is rather biased.

Diplomacy doesn't work in trying to reason with a person with a narrow, self-imposed,intolerant frame of reference. It can be neither appreciated nor understood by them.

I'm happy for you at least that you recognize or relate to them as an acquaintance and not a friend.

Yeah they spend all the time trying to cram their religious crap down your throat but when you tell them to leave you alone you've offended their beliefs what a bunch of hypocritical assholes

It's her choice to be insulted - even though I don't believe you insulted her at all, but was merely straight with her.
I've had some similar experiences with so called entertainment venues.
They just can't seem to stop selling !

You could have handled it in a more diplomatic way but I don’t see what you did wrong. I’ve often wondered why I have to be respectful to people’s religious beliefs but the religious don’t have to respect my (lack of) beliefs.

I think you did well. If you want respect, learn to respect others.

She may not see your non belief as something to think about. Or respect and she can't even understand it.