Yeah, Star Trek likes to be all "racism is a thing of the past" when it comes to humans and pat itself on the back for how enlightened it is, but when it comes to aliens, bigotry and racism is much of the time just accepted as normal. The Ferengi are a great example, frequently being disparaged on based on their ethnicity and it's just played for the laughs like there's nothing wrong with it. In fact, the prejudice is much of the time even validated because they're depicted as being exactly that.
There's an underlying theme here that it's all ok if it doesn't offend real people. But it doesn't actually question the mindset behind racism, in fact it often reinforces it, just externalised to non-humans. Racism reduces entire groups of people to some monolithic lesser other, and Star Trek frequently does exactly that with its monolithic peoples of walking stereotypes. It is anti-racist by means of including all humans in the in-group, but the underlying mindset of reducing the out-group is most of the time not challenged, quite the contrary.
If Trek is serious about being anti-racist, I think it should question this mindset itself (it does on occasion, but most of the time it doesn't). People think they're not racist, but still they often reduce other peoples to stereotypes, seeing little wrong with it because "well it's true, isn't it?". So when Trek keeps reaffirming its in-universe stereotypes, it often reaffirms stereotypical thinking itself.
What exacerbates this is that many alien species aren't just alien, but racially coded in a way that reflects real peoples. The Klingons for example are racially charged with varying shades of Black/Brown/Asian, so the othering and stereotyping of the aliens feeds on and plays into the othering and stereotyping of real-world people. The Kazon being "inspired" by African American street gangs makes their depiction as primitive misogynist brutes pretty problematic. The Ferengi are basically a species designed around antisemitic stereotypes. If Trek wants to be anti-racist, it's not doing a great job here.
As for McCoy... his "pointy-eared" insults may not hit real-world people, but essentially he uses ethnic slurs about his facial features. Imagine he did the same to a person of colour. Thankfully this doesn't happen, but it is the kind of language he's using. It's not a good look.