I can't find the quote, but Norman Rockwell said that the inspiration for his Freedom of Speech painting was a town hall he attended where a man not much liked by the community was allowed to speak his piece, even when the people did not like what he had to say.

I'm not arguing we shouldn't be able to shame or shun (the NYT itself would be my preferred target). I think the idea is that we should aspire to resolving our differences through dialog. What we have now is a crowd of people who feel that dialog is no longer necessary, and that to even simply engage in dialog with one's political enemies is bad and might somehow taint you.