It really isn't about being a purist for me. Black Robert April? Bring it on, I hear the man playing him is an excellent actor. Black Robert April coexisting in the same universe as white Robert April, supposedly being the same character? My brain simply can't make that one work.
It only doesn't work if you insist that there has to be an "in-universe" explanation for any such discrepancies. If you allow for the possibility of occasionally acknowledging that, well, yeah, you're watching a theatrical production and not reality, then it all makes sense.
Sometimes, "Oh, they recast the part" is the only real explanation you need.
A classic example: In FRANKENSTEIN (1931), Elizabeth is a blonde played by Mae Clarke. In the direct sequel, BRIDE OF FRANKENSTEIN (1935), which picks up moments after the previous movie left off, Elizabeth is now a brunette played by Valerie Hobson.
Does this mean that BRIDE is not really set in the same continuity as the previous film? That we're dealing with a completely new timeline? Or do we need some torturous explanation for why Dr. Frankenstein's fiancee somehow found time to dye her hair while the Monster was on a rampage? Can our (abby normal) brains not make this work?
Or maybe you just shrug, suspend your disbelief, and accept that it's the same character in the same timeline, which is clearly the film's intent. Because that's how movies and TV and theater have always worked.
The phrase, "suspension of disbelief," exists for reason. It's fiction after all.