So my question is do you see any problems with or anything wrong with giving better customer service to people who I think might be trans?
I don't see any problems, personally. It's what I would do, although I'm trans myself so that might make a difference depending on the circumstances. I mean... that sort of tendency for me at least feels like such a natural thing, there would probably be a direct correlation between how much (presumably extra) effort I would put into my job and how far the customer(s) is(are) from high amounts of privilege. (that I could tell anyways).
I'm not really sure what it would mean if that was a bad thing. Surely you could do it incorrectly, but hmm...
What it would be like on the other side of things though... Personally: I really have no idea. To be honest. But thats because of social anxiety and autism and not because of being trans :+. I mean, if the circumstances are right, someone saying "hey I like your shirt" can send my brain spinning so... (Not that putting in extra effort, Quixotess, would equate to complimenting people's shirts, but, someone being nicer then I expect can really confuse and fluster me.)
More in general... I've heard experiences from one of my partners where this sort of thing happened and they appreciated it, and I know I would appreciate it too if I was in the mental state I'm in now XD;