I'm going to say there are plenty of other variables at play here in why there is a lag.
https://www.kff.org/coronavirus-covi...ace-ethnicity/
In this data set from early December we see that there is no real statistical difference between whites and hispanics but black people the rate is at 50%. However, it needs to be noted that the gap between vaccinated rates for black people and vaccinated rates for white people decreased by 14% points when the vaccination eligibility was opened in April. This tells me there were occupational reasons and age eligibility reasons for the discrepancy. Looking at figure 3 there was almost a plateau for white people but it looks like Omicron has created a bump but it also looks like vaccination rates in black people are currently headed toward a plateau as well.
Ther is also this data set which shows lags in vaccination rates in counties that supported Trump.
https://www.kff.org/policy-watch/the...ination-rates/
Almost at a 13% rate difference. According to figure 1 it is the exact opposite of the increase in rates we see for minorities in April we see a decrease in rates in Trump counties which is interesting. To me it is definitely politically driven whether it is Biden's policy or Trump's push of a hoax is debatable.