There certainly are disturbingly racist takes out there. I took a look at the comments section of that video from earlier:
If I was being really paranoid, I'd say "yeah of course they replaced the first Captain of the Enterprise with a black man...just as they replaced the first ever Doctor Who with a black girl." As has been said MANY times already, this isn't about equality or representation, it's about claiming what others had built. It's about saying "this is ours now" because they can't or don't want to create their own characters.
Black people are stealing Star Trek from its rightful owners, white people. Sure.
Now, obviously, YouTube comments are a reliable cesspool of bad takes and regressive politics, and I wouldn't have gone there looking for a black swan existence proof otherwise. I'm not characterizing the whole Trek fanbase here. Point of fact, that was the most overtly racist or angry post I saw in the first couple screenfuls of comments, and I saw one "ha, get over it" post on the way there, with much of the rest in roughly in the "just make a new character" group or joking about a canonical explanation for why he's black now.
People lightly snarking at the choice, or calling the writers dumb for not using a different name, though - how many of that majority are consciously motivated by an opinion they recognize would be considered racist, but aren't saying so? I'm betting it's not all. I'm betting it's not none. I'm betting a lot more of them, consciously or unconsciously, are reacting to something that feels like "typical forced diversity" that their favorite talking heads have told them is bad and cheap and pandering. They don't care about the race of the character, but they also don't care about racism or representation, and they're more likely to criticize a TV show for rocking the boat than they are to call out the racists in the discussion. Enlightened centrists concerned about the assholes on both sides don't tend to be allies of representation. They want you to take your politics out of their franchise, and if putting in black people brings politics with it, they ultimately want you to get rid of those, too.
As for telling people what they *really* mean: I was raised by parents and have been around all sorts of people who *really* meant things. My stepfather was quite threatened by the presence of Starbuck in the BSG reboot as a gender-nonconforming woman. He would not have described himself as such. What he told me instead was that if they wanted to write her the way they did, they should have kept her a man instead. I think people who are uncomfortable about women or racial minorities taking on certain kinds of roles, for reasons they might not really understand themselves, can massage those feelings into something more acceptable. It's not that the reaction they're having is based in a racial bias, it's that they're defending canon or calling out pandering or tokenism and so on. Maybe not everyone who makes those kinds of arguments is motivated by racism, but we expect the converse to be true, that people who are motivated by racist ideas are going to tend to sound like that. If you've been burned enough times by people who sound like that right up to the point they turn heel, you learn not to take everything at face value. And I mean, I'm white, I have the privilege not to experience that as regularly or seriously as a lot of folks.
Even if someone is interested in protecting canonicity, which as I've said I can't fully relate to because that's not something I value, I really do expect them to at least have some awareness that old media can have baked in biases that they shouldn't be protecting. Obviously, Captain Pike in The Cage is canonically sexist, and no one's upset that they broke continuity to change that. Meanwhile I've heard black D&D players talk about getting into a game in old versions of the system, and being told they couldn't play a black elf because black elves are evil. The other participants are just lore purists, but the lore in this case is racist and they're not self-aware enough to see the problem with defending it.
So no, you can't call someone "racist" for wanting those kinds of guys to get over it or die mad about it. At worst, they're making a false positive assumption in a pretty plausible situation, usually in response to people who are themselves having an immune response to what they call "woke" or "forced diversity" or whatnot. Calling them "racist" is pretty much the same as those comments on the video in the vein of "What if they made Geordi Asian?" - the fact that you're assuming an even playing field where everything is symmetrical and reciprocal is the problem.