Doxxing is the release of private contact information and personal details. Was his home address made public? His personal mobile number? His private email address? No? Not doxxing.
Public shaming of shameful public behaviour isn’t doxxing. This asshat chose to prove himself to be a racist asshole in public. He was publicly outed as a racist asshole. His business, which serves the public and has a publicly available feedback page, has been tagged with warnings to his potential clients that he’s a racist asshole, because that’s what he is.
And that’s fine, because the public’s right to know that the lawyer they’re considering is a racist supersedes a racist’s right to keep his racism a secret after willingly choosing to air it in public.
He wasn’t doxxed. He’s simply facing the consequences of members of his society choosing not to associate with him any longer, because he decided to tell his society that his behaviour and attitudes were harmful to that society.
He has the right to do what he did. Everyone around has the right to know about it, and to shun him If they choose.