So here's a crazy suggestion....
People in general, and America specifically, have been ingrained with crazy ideas about the human body and how "special" it is. If your girlfriend is going to be working as a stripper, you obviously need to learn to be comfortable with the idea that viewing and appreciating the human body is not a big deal. I don't know where in the country you're located, but take a look at this list and see if there's anything relatively near where you are:
List of social nudity places in North America - Wikipedia, the free encyclopedia. If you can somehow manage it, go hang out topless or naked with your girlfriend, in the presence of others who are doing the same. At first, you'll probably feel uncomfortable, and even nervous, but stay, relax, and eventually you'll ease into it, and into the idea that it's OK for other people to see your girlfriend's body. If you can't manage to find a place to do this, look at lots of nude art, I dunno... just try to think of things that will help decouple the viewing of the naked human form from sex.
Yes, at a strip club it's different - it is absolutely sexual - but I think the heart of most people's problem with a strip club, especially for a guy who trusts his girlfriend, is the idea that viewing someone's naked body is special and somehow reserved. Learn to realize that someone else seeing your girlfriend naked has nothing to do with how special your relationship is with her, and maybe you'll find yourself a lot more comfortable with the idea.
Of course, I could be entirely wrong. Just some thoughts off the top of my head!