I have to confess I've never seen Moonlight, but it's probably at the top of my list of recent films to see. I just haven't had time to watch anything lately.
My one comment is that I think the phenomenon being observed isn't unique to racism or Moonlight or films--I think it's related to a work having a narrow audience and then that audience widening. The observation that "as Moonlight’s acclaim grew, the film’s release widened from 650 theaters (November 18) to 1564 (post-Oscars)" is important.
I've noticed this with blu-rays and books on Amazon as well. I've seen this with certain technical books a lot; initially they are highly rated, and then as word of mouth spreads, and they get introduced as textbooks, and people start mistaking them as introductions to a topic, you start seeing people get frustrated that they aren't what they were looking for, even though the problem is the book was never for them to begin with. I suspect there is something unique about Moonlight, vis-a-vis racism and concerns about "reverse racism" at the Oscars (which in its strict form is undermined by the high critic ratings--you'd have to argue the white guilt extends to critics, who I don't think experienced any change in that one way or another over recent years), but I also think something about going from niche to widely viewed also is relevant.
It would be interesting to compare Moonlight's ratings to other films that had big increases in distribution in a short time, especially those that went from arthouse to widespread distribution. My guess is you would see similar phenomena.
I'm familiar with how to do analyses to examine bias, etc. and as far as I know IMDb doesn't have the fine-grained level of ratings you'd need. For example, you'd want to show that somehow more specific subratings and their relationships with some overall rating changes.
There is rating by demographic, and it would be interesting to see how that might have changed over time--for example, if the demographic groups doing the ratings changed, or if the relationship between demographic and rating changed. I don't think IMDb gives that kind of fine-grained detail.
You could go over the top as much as you want, though--doing topic analysis of written reviews over time, etc.
