Not sure this is still true... what do you mean by "access to the full sub"? On https://www.reddit.com/r/BlackPeopleTwitter/ I cannot see any restriction. And the rules in the sidebar state 'BPT is an inclusive space for POC and allies alike.'
one of the more painful experiences on reddit is spending 30 minutes writing up a post for a subreddit only to hit submit then get your content immediately deleted by a moderation bot ran by the sub's mods for breaking some rule you didn't realize existed or for having previously posted to some other subreddit that the mods disapprove of, even if you were posting a critical comment or disavowing the beliefs in that other subreddit.
Reddit is a platform for communities. Some communities, across all spectrums of topics, find reasons to create a somewhat exclusive environment. They are not required to make space for all views, and that lack of forced-openness is not the same as censorship.
/r/conservative does the exact same thing, why the handwringing about that sub in particular?
I feel it's important to note that a similar restriction focused on any other race, even other minority races, would probably be banned within a week of creation.
there is a disturbing pattern the administrators have of proclaiming their love for freedom of speech in a post, receiving huge backlash, then going on a banhammer rampage. it's happened at least four times /in my memory/, and probably more throughout the site's entire history.