Option 2.
First thing, many traditions existed since the beginning of social interaction, including slavery. We've not entirely removed that, but most people agree it was overall a bad idea. Human sacrifices to the gods also were great back in the good old days, but I do hope they have vanished long ago.
Secondly, has it occurred to you that popular opinion may sometimes happen to be wrong? Lynchings were carried out based on popular opinion, and maybe sometimes the man who died had actually committed the crime. But we can't really know that, can we?
Now, I'm well aware that "we'll stop talking with you" is not the same punishment as "we'll hang you after having tortured you". But IMHO no punishment at all should be meted out unless every step has been undertaken to make sure the accused is really guilty.
That's why humanity introduced another tradition, even if it's not as ancient as punishment based on opinion. It's the rule of law, fair trial, rights of the accused, beyond any reasonable doubt etc. etc.
Note I'm not saying I have doubts about the culpability of the guy in this case. That's beyond the point. The point is that in "word gets out that you're doing something nasty", the "word" is far from being guaranteed to be true.
Social media makes it easier to be social? Maybe. Some sociologists think that we are still wired to live in a village, or in a large tribe before that. That there's an upper limit to the people we are able to consider and treat as knowable. And that online interaction still does not hold a candle to the personal interaction we're built for. If they are right, then you might consider that shaming and avoiding a villager you knew since you were a kid, based on the "word" of other people you knew since you were a kid, was probably a choice that would be based on a better knowledge of the guy and of the talkers, and not taken as lightly as on social media today, based on the words of a media source and about a guy you had never heard about before.
So maybe social media only makes our social interactions louder, more far-reaching, and less balanced.