Which one of these "I don't like it" statements is valid, if any?
A. I don't like it because if you are a centaur then many of the dungeons and boat travels and mountain climbing adventures I have might get you left out for several sessions.
lol what? You know horses can go on boats, and climb up mountains, right? Especially horses as small as a 5e centaur.
B. I don't like it because if you are a loxodon then every single town you walk into you will become a circus freak show or worse yet, be hunted by groups that see your tusks as secret ingredients and aphrodisiacs.
That's some wild nonsense that the DM could easily just not do. Sounds like an edgelord DM, or one that is just not very imaginative. Either way, not a compelling reason.
C. I don't like it because in the world I have set up the race you have chosen is the villain. They have burnt, murdered and pillaged for hundreds of years. People will not trust you. People will not like you. And in most cases, for this adventure set in a war torn city (thanks to your race), people will try to arrest you or worse, kill you. And no one will care.
Gross. And an edgy exaggeration of how people actually behave. Sure, such things happen IRL, but even in 1940 you could go shopping in plenty of places the US with a German accent without getting arrested (lol wut) or physically attacked, and if you were attacked, there was a solid chance that someone would object. If you also happened to be an obviously dangerous person, in a group of Americans and Brits who are also obviously dangerous? Chances of your being bothered are pretty low.
D. I don't like it because you are magically trapped on a continent where everything is set up. The DM has set up the kingdoms, the people, everything. They have not seen outsiders for hundreds of years. The only strange things they see are creatures. Creatures that look like your tabaxi, in the form of a weretiger. The DM explains they can't just make a race living somewhere in the unknown.
Arbitrary nonsense, and bad worldbuilding practice, unless you're maybe running a one shot or short limited campaign for strangers. Most people don't play with strangers as their primary play experience, so most of the discussion will naturally not take that scenario into account. It's neither the norm nor the ideal. But even when I ran DnD for kids at the public library, before Covid, I'd consider it a weakness as a worldbuilder and a storyteller to intentionally create a world scenario in which I "can't" add anything to the region of play.
E. I don't like it because personally, it doesn't fit within my sensibilities. It just seems silly.
Only acceptable in very tightly themed campaigns, and even then I'm gonna rib the DM a bit for not being able to past their own associations and see tabaxi as more than anime catgirls. I won't be a jerk about it, but the occasional joke will be made. In a less tightly themed game? Nah. Get over it. It shouldn't matter that you dislike tabaxi. If a person can't have fun running a game with a single race they dislike, i don't trust that person to even be fun to be around, much less run a game well.
I didn’t ban any races (except for yuan-ti, aarakra and winged tieflings for being overpowered).
None of those are at all overpowered, but okay.
I know of at least one table where the (all-male) people at the table have rules about no female players and (GM excepted) no cross-gender characters. That I can tell, the players aren't virulent misogynists. While I ... disagree with the rules, I have no problem with the table establishing them.
Virulent is an irrelevant qualifier. It'd take some pretty weird circumstance for a "no female players" rule to not be misogynist.