While that may sometimes be the case with social media, I don't think this is one of those times. This dude said some pretty racist things, and previously he would "get away with it" because nobody really heard him. IMO, he deserves to be called out for his nonsense and shown how it makes the people he insults feel. Bright light is a good disinfectant that way.
I dislike with the way it was handled, because it was predictable that it would inflame all sides and cause people to dig in. The most likely outcome here would seem to me that the guy goes underground and learns to make his comments anonymously. I'd speculate he probably feels picked on right now and will be even more extreme as a result.
At least he had the guts to address his comments(as unfortunate as they were) specifically to an individual and put his name on it. I would tend to believe he didn't think he was "getting away with it," as much as scolding a kid who he thinks should behave differently- Like an extreme, way-out-of-touch version of a Bill Snyder note. He is probably, like most of us, living in an echo chamber surrounded by people who endorse or at least enable his thinking.
If, instead of someone doing an Insta-Shame blast, the young man who received the letter(or his coach) had invited the guy to come into the football offices and sit down and talk, maybe they both could have learned something about each other and each come away with more open minds.
You can tell that in spite of his outdated way of thinking, he really cares about the school. I just don't see how it helps advance any solution to the problem by publicly shaming someone who might be a possible convert to a different way of thinking.