Of course, you can attempt to transfer wherever you like. The advice to start with the two Ivy League schools to which you were originally admitted seems reasonable. However, if you don’t like the elitism at an elite school, just transferring to another elite school seems self-defeating. How many chances do people get at these places anyway?
Were I evaluating your transfer application, I would see a downward grade trajectory and difficulty adjusting socially, neither of which would bode well for your success at the next school and both factors seem much more important than whether you are gay or URM which seem mostly irrelevant.
None of that is to say that you should not try. But just like applying for freshman year, you should have some academic and economic safeties in mind e.g. state school honors programs.