Your question focusses very much on the physical aspects of the relationship (okay this is the area where there are problems but the point I am making is that the answer probably lies partly in the emotional and other aspects of the relationship).

Okay so this is part of her beliefs. If you just cut back and expect it to be an eye-opener for her then you may be sorely disappointed. If it is truly part of her beliefs then she won't respond to ultimatums (which seems to be what you're offering). Instead she's likely to be very upset with you for not respecting her beliefs and trying to pressure her into more than she's willing to give.

Which is where the rest of the relationship comes in. How do you feel about the relationship in other respects? Is it growing emotionally closer, do you enjoy her company, are you thinking this is someone that you want to develop something closer with? You might not be thinking of marriage at this stage but are you thinking of her as potentially someone for the long-term or you're not sure yet and are just enjoying dating? If you think there might be something long-term in it then you might want to consider talking to her about her beliefs, not just this one but others, to clarify how you feel about them and to explain to her how frustrating it is to have such barriers. And then maybe you can find a way forward. Everybody has values and morals (whether informed by religion or not) that will affect their views on a range of issues, situations and decisions. Part of getting to know somebody is getting to know their values, them getting to know yours, and working out a way through life that meets both people's needs.

If you don't think she's got long-term potential then maybe you could accept the differences in belief, accept that there's no long-term potential and therefore it's quicker and easier on both of you to draw the line now - it would enable her to find somebody else (more suitable) as much as it would suit you.