people do indeed have the right not just to an opinion, but also they have the right to insist their opinion is correct or factual.

what they don't have is the right to deny others their right to share *their* opinions, which might well be to disagree, or to point out actual facts, or to ban them from the store, or to stop buying their product, or simply laugh at them.

All forums of discussion have basic ground rules in order to ensure a productive conversation. Without that, it's just chaos. The rules may or may not be written and will vary based upon a variety of factors.

I get this from conservatives all the time, that their opinions are shouted down.

Many of these "opinions" are actually scientific assertions. Well it turns out the forum for scientific discussion has quite a bit of structure. We like to see papers and peer reviews. So when you make an end run around those rules, don't complain that you are being "shouted down".