It'll be awhile before we have demographic turnout data for the 2020 election--and therefore comparisons to 2016--that I will feel I can really trust. But embedded in a slide show and report available for the Voter Participation Research Center (VPC) are some interesting turnout data produced by using AP/NORC VoteCast 2020 + Pew 2016 + Census/CPS eligible voter data + official vote counts. I'd say these are pretty good for the time being and as good or better than other estimates that are floating around.
The VPC data were produced to inform their ongoing efforts to tout the "Rising American Electorate" (RAE) which they define as nonwhites + Millennials/Gen Z + unmarried women (with double counting due to overlapping categories eliminated). The analysis is a bit skewed to accentuate positive connections to their campaign which leads them to underplay a few of their findings.
One is that while RAE turnout did indeed go up (+6), it went up considerably less than it did among the non-RAE (+11). Because of this relative decline in turnout, RAE growth in voter share lagged growth in eligible voter share. While they do not provide a specific turnout figure for nonwhites, it is notable that they estimate nonwhite voter share was flat across the two elections at 26 percent, despite a 2 point increase in nonwhite eligible voter share. And they estimate black voter share actually declined from 12 to 11 percent, presumably not because absolute black turnout declined from 2016 but rather that it went significantly less than among other groups.
Much food for thought in their report and slide deck, though I would be wary of some of the interpretations, particularly around contributions to Democratic margin which are lacking a comparison to 2016. That said, this is still interesting data to sift through while we wait for better stuff to come in.