Several reasons. The initial roll out in most states were hospitals and healthcare facilities, which I think are dominated by white people.
Then the roll out was only in a few locations in each county and the locations were not in many urban centers but rather you had to be able to drive to them, so the poor and people who could not drive couldn’t access those locations.
Many states require appointments for shots and the poor and other minorities are less likely to have all the information to make the appointments or the internet.
There is some reluctance to get vaccinated among minority communities at least for now. Some wanted to wait and see.
I was just looking at this in my state. See page 2 https://www.floridadisaster.org/globalassets/covid19/vaccine-info/2021feb/vaccine_report_20210226.pdf for vaccinations distribution by race in FL. There have been some irregularities in our vaccine reporting, I’ve been following it closely and the number of first doses was being recorded incorrectly initially from what I can tell, but I don’t have reason to think the demographics are recorded incorrectly except to say with do have a lot of “mixed race” in the state. A misnomer, but I’ll use it for simplicity.
The document shows 6.3% of the people vaccinated first dose are Black if my math is right. The Black population in FL is close to a 16% population. There is an “other” and unknown category that is very large combined, so I think the Black number is likely underreported, but still should not be ignored.
I read recently FEMA will have two mobile units in Florida to vaccinate in “underserved communities.”
Initially giving contracts to Walgreens and CVS to vaccinate in long term care might have inadvertently hurt minority/poor communities since drug stores are in multiple locations all over cities and more easily accessible. Although, I do think the first month it was prudent not to vaccinate in pharmacies and grocery stores.
Edit: one other possible reason is Black life expectancy is shorter than White people and a lot of states started with 75 and up for eligibility