While sex is a natural part of life, you aren't going to die from foregoing it for a period of time. She might think you're an asshole, but breaking up is the best outcome for both of you! Imagine the following scenario, though: Remember that relationship is ultimately about sacrifices. This way of absolutist thinking brings unnecessary issues about sex. You are not a "dick" because you want physical intimacy from someone you are thinking about spending the rest of your life with.
Feel free to make mistakes but don't make a mistake that can mess you up in the long term.
Please Remember To Remain Kind and Civil
I'm in exactly the same situation as OP although she does do a few things but no sex but it's been 4 years, I love her with all my heart but I don't want it to be a waste if she leaves me. But i do have something new to add, which would be to try discussing what and why her reasons are for celibacy. If it's a theological disagreement then there's often no wiggle room. It's not your fault or hers. I find it stranger that someone would interpret 'celibacy' as 'all sex goes, as long as the hymen remains' or whatever. I just realized that who I was was, and always will be, changing. But being I don't fall in love quickly, that probably wouldn't happen.