Every family's different, but homophobia in AA culture can be especially ugly because the belief is widespread that being bi or Gay is only a White thing. Faith communities have also been even less supportive than most White (especially Jewish) ones. Not that the hypocrisy is any lower - just look at "Bishop" Eddie Long to see what I mean.
There's a large number of AA's in both my work and social lives, and what I've found is that they feel like I have more street cred due to my being same-sex-oriented. In a weird way they embrace me more warmly as a White person because I'm no stranger to ignorance and discrimination. YET the scenario completely changes when a "brother" comes out, and many times more so if he defies Gay stereotypes.
Pops will have a worse time, much more likely, than Moms and the sibs. Men of all shades do as a rule when it's their son who's coming out. And men of "all shades" don't have extremists within their culture who rant on about the genocide of the race being at hand. Also, most folks who watch those obnoxious Tyler Perry movies are also Black like he is, and are all too willing to laugh at "Madea" flouncing around parroting moralistic Bible babble condemning Gays, and women who control their sex lives, and so on. Madea isn't a threat because "everybody" knows Tyler Perry is no fag (ahem) and only dresses up to be funny in his films. But the repressive messages sent out by the films ARE a threat.
Although PFLAG has historically been a White organization, there's been a lot of work done to collaboratively reach out to communities of color. Some major cities with large AA populations (Chicago, NYC, and Boston to name three) have succeeded in launching separate support-group chapters that focus on assisting "minority" LBGT's and their families. You can find out more about this group, and download reading materials, by visiting http://www.pflag.org as well as attending a meeting in person.
Good luck with your dad, and Happy Juneteenth in advance.