Wow, blaming political correctness for the idea that black ancestry makes someone black. You might find this to be enlightening:
https://en.wikipedia.org/wiki/One-drop_rule
https://en.wikipedia.org/wiki/Hypodescent#Hypo.2Fhyperdescen...
The idea that a mixed-race person is considered to be a member of only one of their parents' races long predates people's unwillingness to use "mulatto."
And the idea that people must call him "black" because they're not allowed to say "mulatto" is absurd. "Mixed" would describe it without causing any offense, as would "half white, half black."
I remain amazed at how insistent some people are that the lingering consequences of centuries of racial injustice in this country are somehow caused by "political correctness" in the past few decades.