Should they have? No, probably not.
Yeah, I think it's definitely fair to question whether or not this was a valid arrest, but that's not really the point. The point is, valid or invalid, was the arrest made because Gates is black? Given how this situation obviously played out, there's ample evidence to suggest he was arrested because he was being an ####### to a cop, and no evidence
at all to suggest it was racially motivated. Anyone saying it was the latter, including Gates himself, is just a race-card-mongerer, and a big part of the reason why the divide remains where it is today.