Since krellin doesn't know what self-identification means within the context of Christianity, he goes on a rant about nothing instead of asking for clarification. As a result, he completely missed the point. Maybe next time he'll ask for clarification. Probably not. I would appreciate it, though; it makes for some two-way civil discourse as opposed to krellin shouting at his computer screen.
Self-identification within Christianity is the idea that someone can be Christian without any regard for their beliefs or whether or not they belong to any major (or minor) Christian church. It suggests that someone who claims to have come to Christ is Christian, whether they are the perfect human being or a serial murderer, and whether they know about God as a trinity or if they even believe in a universal God at all. Many Christians, generally for the better, are growing more inclusive within their religion, thereby diversifying the religion and also destroying the idea that the various institutions within Christianity decide who is in and who is out. It is self-identification that has allowed hundreds of smaller denominations of Christianity to exist (Mormons, Amish, etc.) on top of the three major denominations.
The same principle applies to gender. It's analogous. If one accepts that gender is a) a choice, one that, like our name and maybe our religion, we are typically assigned at or around our birth, b) a social construct that has been ruled over by various institutions for many generations, and c) should not be ruled over by said institutions anymore, then accepting the reality that some people's gender and sex don't match up is not difficult. This is the same principle of self-identification.
In general, it falls in line with the "who the fuck am I to decide for someone else" mindset. It's quite libertarian (lowercase L, though it should be applicable for the uppercase L too).
As an aside, private businesses have always been afforded the right to refuse patrons for just about any reason. However, private businesses are also subject to the laws of the land, which may or may not, depending on the place, include anti-discrimination laws, and if they break those, they should be punished accordingly. If a private business owner has the audacity to refuse to serve someone based on such petty moral disagreement, specifically in your example over the fact that the patron is gay, then the rest of the community and whoever else feels like chiming in also has the right to shit on that business's porch. Two-way street. How joyful our world would be if we had to drive all the way around the whole fucking thing to park one block to the east.