I can tell you that here in Washington State when we had battles over anti-discrimination laws, domestic partnerships and eventually marriage, the large majority of Democrats supported gay rights while the large majority of Republican opposed them. I believe this has been true in many other states as well. That is a real difference on an issue, not just being "jerked around."
I would not say that all gay Republicans are self-hating. Some in my state have done good work on LGBT issues. Pablo Monroy, for instance, filmed an excellent video in favor of R-74.
http://www.huffingtonpost.com/2012/06/25/gay-marriage-washington_n_1624913.htmlThat said, it is easy to find even more counterexamples: Larry Craig, Jim West, former WA state legislator Richard Curtis, Ted Haggard, Phillip Hinkle, etc. we could go on and on. These folks are either Republican politicians or affiliated with the Republican party. They denounced LGBT and LGBT rights and/or voted against them while engaging in gay sex. So yeah, I would call them "self-hating." Perhaps one can see how gay Republicans have developed a negative reputation in the larger LGBT community.