Depends on intent, to some extent. Costumes can be racist. The original blackface is/was racist, as it was mocking. The core concept of pretending to be another race isn't racist in and of itself, though. White people can wear black costumes, and vice versa, without it being racist. The picture in the OP? Not racist. But if the white costume was something pushing negative stereotypes, done from a hateful place, you could argue that would be racist. Again, it's not about the race swap, it's about the race hatred.

If he dressed up as the 'white hillbilly' stereotype, for example, with the buck teeth, overalls, and something like a 'I &##$ My Sis" shirt...yeah, that would rightly raise some eyebrows. But even then, he could just be having fun. That does actually sound like a funny costume, and costumes used to be more wild, and I think we need that back. Nowadays you can't even dress up as cowboys and Indians, and the like, without some progressive throwing a fit.

As others have pointed out, it's the double standard that's the real issue. I personally don't care at all if you do a race swap costume, and I don't really care if you do a racist costume either, of any race. Be offensive, who cares.