I'm not certain of Walt's role on the team, so I'm not sure about how I feel about him turning off replies.
His Twitter bio says "Editorial Content Producer and Reporter", which, if that is his role, means he's got no obligation to subject himself to the wave of shit that I'm sure comes his way.
If he were part of the PR team, then I'd say it's probably bad taste to have the Public Relations team block commentary (no matter how inane) from the public.
However, the team account regularly retweets Walt's updates during the games (rather than use the PR account), so in that way, he seems to have a bigger role than what's listed in his bio.