A Pew Research Center 2017 survey gives us some estimates: Black gun ownership is lower than white gun ownership—but not by much. For whites, 36% of respondents report that they own a gun personally, and 49% report that they live in a household in which someone (whether they or someone else) owns a gun. For blacks, the numbers are 2/3 of that: 24% and 32%. (The numbers are lower for Hispanics, 15% and 21%.) In raw numbers, there are about 40 million blacks in the U.S., so about 13 million (or likely about 10 million adults) live in gun-owning households.

This seems to closely track different gun ownership based on ideology. Blacks generally vote about 90% in general elections for Democratic candidates, so it's fair to say that they are generally Democrats or lean Democrats. Among all respondents who said they were Democrats or leaned Democrat, the numbers were 20% personal gun ownership, 30% household. Assuming that the great majority of blacks fall in this political category, white and black gun ownership among Democrats and Democrat-leaners seems to be virtually identical.

But in any event, there are lots of black gun owners out there, just as there are lots of Democrat gun owners. I can't speak to what fraction of gun rights activists or gun rights enthusiasts are black—it's certainly possible that black gun owners are on average less likely to focus on this issue politically than white gun owners. But it seems pretty likely that many black gun owners do care in considerable measure about their right to own guns, whatever fraction of them might or might not show up to, say, gun rights rallies. (Naturally, this tells us nothing about what is good gun policy; I am speaking here only of demographics.)