This is like trying to debate religion with a fundamentalist--you can't win, even if you're right.
Don't mention what happened for a while and then see if maybe she's gotten over it. If not, try apologizing--say "I'm sorry, I shouldn't have gotten so upset, you're entitled to believe whatever you like." Of course, if she still tries to insist that you AGREE with her...that may be problematic.
IMO, someone who's so rigid in their thinking that they can't see others' points of view is very difficult to remain friends with, because she probably takes it as a personal attack when someone disagrees with her about anything.
I don't know if this helps, but...I know people like this, and in my experience remaining friends with them is extremely draining after a while.
Hope you find friends who are a bit more open-minded.
_________________
The existence of the leader who is wise
is barely known to those he leads.
He acts without unnecessary speech,
so that the people say,
'It happened of its own accord.' -Tao Te Ching, Verse 17