The studies do support a lot of the claims made in the video within the first half of the Project Veritas video. Studies of babies reacting to skin color and other social cues goes back decades, it's not really controversial, and it's not Critical Race Theory. Tribalism and defining in and out groups is fundamental to human social organizations, and that's literally among the first things kids pick up.
That's why I think the PV video is very weak, because it starts by presenting correct information as outrageous. Babies and young children pick up cues about in and out groups. That's not the problem. The problem is it doesn't look at the full scope of how people think. It's similar to the implicit bias tests, which are used to claim people are bigots by flashing images of different people on the screen, and then measuring how the subject reacts to people of different races. While it's true that most people show some degree of favoritism, it's literally just measuring how people react in the first instant. It doesn't account for all the other processes that occur in our brain. There are layers of responses that occur after that first instant, where different parts of the brain jump in, and react to that first reaction, often completely overriding it. A lot of what the pre-frontal cortex does, for instance, is overriding the quicker response of the amygdala. This doesn't happen at the conscious level, but phrased in conscious terms, it's basically the equivalent of reacting negatively to someone, and then realizing your reaction was unfair, and trying to compensate. Now the initial reaction does matter -- if you're deciding whether to shoot someone, the higher parts of your brain may not have time to react -- but in most social situations, it's almost completely irrelevant, because that initial reaction will be overridden. It's not amoral to correct an initial response. In fact, you can make a strong moral argument that someone who does that is more moral than someone who didn't have the negative response in the first place.
So unless you look at the full picture, you're just cherry picking details to support a narrative. The different parts of the brain develop at different developmental stages in babies, children, and young adults; and they need to all be considered before you can draw conclusions about bias.
If anyone's interested in how the human mind works, including moral development, I'd recommend Behave by Robert Sapolsky. It's a massive, magisterial tome that covers everything from neurology, to genetics, all the way through psychology and culture.
The second half of the PV video is more to the point, because it's highlighting a lot of the loaded jargon being used, the improper conclusions being drawn, and the questionable recommendations of the trainers. I would have liked a deeper dive, because it mostly just comes across as gibberish with bad intent.