When the "other side" is arguing in bad faith, you're damned if you let them speak and damned if you don't. Someone like that isn't going to play by the rules of logical, rational discourse - such as sticking to the facts - so there isn't much to be gained by letting them speak versus not giving them a platform. I point you to Holocaust denialism, which has a long, rich tradition of ignoring, obfuscating, or concocting elaborate alternative explanations for any truths that run counter to their dogma. Or for something more benign, the flat earth movement or the Apollo landing conspiracy theorists.

It's easy for a bullshitter to make up more bullshit, and people love to believe "contrarian" bullshit so they can appear smarter than the next guy. Refuting bullshit takes time, energy, and effort that could be spent on more productive activities.

It's absolutely a worry that legitimate contrarian speech (I get that that's an oxymoron to some people) might be suppressed. But that's not what's currently happening.