Hard to say. “Same” to mean of the same type or of the same intensity? To me the answer would be Same Thing, Only Different. For example, it has happened that businesses have forced their trans employees a restroom that is only for them so that they do not use facilities labeled by gender. I know that has been challenged, but I don’t know if there are any specific legalities.
On the other hand, gay people may be discouraged from bringing their partners to company functions in very subtle ways. Depending upon the orientation of the trans person, that may or may not be similar.
I think the only way to really answer the question would be on a situation by situation basis…
Regarding what happens for trans people, and specifically trans women, in general society I think when people are discouraged enough, abused mentally and physically enough and forced into the off-book illegal economy you become distrustful and resentful of everybody. It doesn’t make any difference if they look like you or not. Perhaps the thought process is if I can’t be OK and lead a reasonable life, why should you get to do that? In general, our reputation internal to the community and external to the community is not good. Whether it is true of a give person on not, the perception is out there and it hurts us.
When it come to politics, it is strictly a numbers game. At 5%, the gay population of the US is at least 16,000,000. The trans population in the US is about 2,000,000; 1,400,000 adults and the rest yound people. Considering how long it took for gay folks to be free to enter the military and to have marriage equality, how many decades are we talking about for trans folks?