I've seen guys join the JWs in order to 'win' the girl. Some actually succeeded. Joined the JWs. Got baptized. Got the girl. Married the girl. So - they got the girl, but now they're in a cult. Unless you want to be in a mind control cult, that dictates to you most every facet of your life, it's not worth it. Of the guys I know that did it, things didn't work out in the long run. Divorce or misery... sometimes both.
If you have to change religions to please the other person, you're caving to them and are not being true to yourself. If you're not true to yourself first, you'll never be truly happy.
It seems to be a simple solution: RUN! but it is the best. Do not get romantically involved with anyone who won't return affection unless you join their religion. JW, Mormon, or any other religion.