I think "Star Trek is progressive" is the crux of the matter here. That's its legacy, that's how it likes to see itself and how it likes to be seen. And it definitely is at times, but at others... not so much. Or even both at the same time. And if one takes this seriously, I think it needs to be scrutinised how progressive it really is, because there's a lot to unpack here.
And just to be clear, this is (in my opinion) not about condemning Star Trek as a whole, but to observe critically where it succeeds and where it fails, and how it should do better in present and future. Trek can still be enjoyed without turning a blind eye to its issues.
If one is serious about being anti-racist (as Trek often wants to be), one can't stop at the surface level. There's a danger in just labelling something as "progressive" and be done with it. It's easy to call out something as racist when it's flying the Confederate flag. But when racist ideas (conscious or not) are perpetuated under the banner of progressivism, people quickly turn a blind eye, thinking all is fine because hey we're progressive. This complacency can actually normalise the racism that it thinks it has overcome.
Racism isn't just burning crosses. It's also subtle and not so subtle tropes, stereotypes, preconceptions that aren't even recognised as such, and are widely accepted as normal because it's what we're continually being fed by society and by the media we consume--and Star Trek is no exception. They may seem "harmless" or "inoffensive" to many, but the "normality" of it has real world consequences for the people in question.
If one says "Bah I don't care", sure, you do you. But Star Trek does not say that. It set out to be boldly anti-racist in the time of the Civil Rights Movement, and consciously averted racial stereotyping in characters like Uhura, Sulu and Daystrom. Kirk explicitly tells Space Lincoln that they fixed racism. At the same time, you get brownfaced and bronzefaced Klingons, variations on the Yellow Peril, and many more not-so-progressive racial stereotypes.
They made conscious decisions in giving the role of the leader to look up to to a Black person in DS9 and to a woman in VOY, and it's frequently pointed out how bold and progressive that was. And while that's great and commendable, that doesn't mean one should blindly accept the things that are very much not so great. Quite the contrary, I think this image of a "beacon of progress" means it should be scrutinised more, not less. And again, with scrutiny I mean examining the bad without dismissing the good.
I think the honest examination of these issues does much more than just discuss Star Trek. It's also a conversation about matters of both overt and underlying issues of racism, sexism, homophobia etc. in media, society, liberal politics and so on. And about taking a closer look at your own skeletons in the closet even if you think you're progressive. Star Trek is very interesting in itself, but also a great model case for examining these things in general.