ultimately if you play the music and it sounds good it IS good, I think everybody would agree - I'm a big fan of Ralph Ellison in this respect who said, more than once, that culture ain't genetic but passed on culturally, etc. My favorite example, of course, is always my late, lamented, crazy friend Dave Schildkraut; white and Jewish and, according to what Dizzy said to me in the late 1970s, "the only alto player to catch the rhythmic essence of bird". (italics mine, of course). Like it or not, racial politics often play into our musical evaluations; my favorite are stories about the old time music collectors of 78s who would sometimes withhold judgement on a recording they heard until they knew whether the performer was black or white; in this way they could judge the "authenticity" of the performance more accurately. Well, there's enough in that action for 2 or 3 books.
I also remember Bill Triglia, white and Italian, pridefully telling me he could play the blues as well as anyone - and he was right (as I've been researching my current blues history I found an amazing little solo he takes on a blues with Lester Young from a 1950s broadcast).
and the blues seems to have been a point of pride for some white musicians -
"I went up to Monk after he played a tune and I said 'Monk let's play some blues.' I wanted to show him I could do it."
-Dave Schildkraut recounting a night at one of the after-hours jam sessions in the '40s (mighta been Mintons, I can't quite remember)