I don't know if your girlfriend is anywhere on the ace spectrum, but I am, and your story make me wonder if that might play some part in your situation. There are plenty of asexual, gray-ace, etc. people for whom attraction and desire are dependent on very specific factors/only apply in specific situations, and who can go long periods without sex and then happily reengage with it. Maybe this is the case for her, maybe it isn't, but I wanted to offer this perspective. I am asexual, and I have a girlfriend who is not. We are not intimate (although I know this is not the case for all ace folks.) Our relationship works for us at this time.
If that fact changed, and my girlfriend came to feel that mutual intimacy was very important and necessary to a relationship, we would ultimately have to break up. This wouldn't be anyone's "fault," not really-- not mine for not wanting to engage in intimacy, not hers for wanting something very personal and fulfilling and important for most humans, not out of lack of respect or love or willingness to make the other happy, but because our fundamental needs have become mismatched.
Your girlfriend's reasons don't really matter, in this case-- whether she's lost her sex drive, a matter of personal conviction, religious mores, she only wants to get it on in the confines of holy matrimony, whatever. They are all good, fine personal reasons to not get intimate, and you can love her and respect her wishes.
And your reasoning-- wanting to be intimate and know you share intimate chemistry and compatibility before tying the knot-- is a very good, valid, fine reason too, and to be respected too.
This isn't a matter of 'fault' or even being unrealistic-- your girlfriend may be perfectly accurate in her judgment that she'll be able to happily and enthusiastically be with you after you've exchanged vows. But you're mismatched, fundamentally incompatible on this point, and couching it in terms of "if only she'd stop being selfish and do XYZ for you" or "if you really REALLY cared about her you'd stop being selfish and just propose already" is only going to hurt the both of you. I think you should take a break from each other, at minimum, and work from there.