Would you really feel the same way if it were GUTS, Grace or Victory Christian?
I think that if the invitation was to a place other than their place of worship, you'd be correct. Meet the people, not their religious beliefs.
A couple of years ago a friend's dad died. I went to the service even though it was not of my religion, but couldn't help noticing that the friend's wife was outside the church, waiting in the limo. Her religious beliefs would not allow her to enter, even though she loved and respected the deceased.
After the funeral we had lunch together and both I and the friend's wife had a good time talking to the priest.
I didn't agree with her behavior, I understood it.