This is a couples communication issue more than anything.
Just as you want respect for your eating "culture", your girlfriend wants respect for hers. (Now is not the time to bombard her with online links, books, or anything else seeking to convert her.)
First thing to do is make a list of all the meals you can eat in common. It sounds like she will eat fowl and fish in terms of animal proteins.
So build a list of a few primal dishes that she will eat, and therefore you will eat. Make those meals the centerpieces of your dinners, say 3 or 4 nights a week.
The other eat-home dinners can be "to each their own." You cook YOUR meal, she cooks hers, and you eat together.
If the budgeting issues are part of this, pool your resources for your communal meals, and then divide up the kitchen in your Primal Zone and her SAD Zone. Do this with respect.
Lead by example. As you continue to get healthier, leaner and fitter, she may just join you. Be patient. I assume there are qualities in her that are special to you. Don't let the kitchen ruin the bedroom, if you know what I mean. Just approach this as a problem to be solved, where neither of you is WRONG and NEITHER OF YOU needs to change.