In a 2 party system like the US, voting for a fringe candidate in a tight race is essentially handing your least-preferred alternative a free vote. For example, people voting for Ralph Nader in 2000 contributed to getting Bush elected (whether you consider Bush's win good or bad is irrelevant to my argument) especially in swing states like Florida.
People sitting in the middle who do not feel particularly bad about either main candidates (or who feel equally bad about both) can afford a rational choice to protest by voting for a 3rd party during a tight election.
Black Americans may, in 2016, have felt significantly more apprehensive about Trump's candidacy than Clinton's and voted accordingly.
Now, how that works wrt Electoral College mechanism in non-competitive states, as Alabama would have been in 2012, is harder to assess. It wasn't a tight race locally, so a protest vote wouldn't have mattered much, unlike in 2000 Florida.
But even a non-competitive State-level contest may still feel competitive if the race is close at a national level and may compel people not to "waste" their vote.
In any case, with Obama on the ticket, Black voters had an obvious reason to vote preferentially for one of the 2 main candidates, so neither 2008 or 2012 are particularly good elections to use to investigate your question.
Another possibility is that 3rd party campaigns, which typically have less resources and a narrower base, can't, or do not bother to, court minority votes sufficiently assiduously and thus mostly only get votes from the majority ethnic groups.