What opinions deny other people's rights?
One example I have in mind is from several years ago and I can't find the details. A restaurant owner and their family were harassed and threatened online and IRL until the owner had to fire their own child... because something like 5 years prior to that, the child had made a social media post that was considered racist when they were 13 years old. That child's post would certainly be in poor taste, and very reasonable made people angry. But their opinion didn't deny anyone their rights, as a 13 year old has no power to affect other people's rights. A post on social media doesn't affect other people's rights, no matter how disgusting it might be. Yet the parents were harassed and intimidated into firing their own child for something that had happened years ago.
Another example was from either Oregon or Washington, probably a decade ago at this point (time flies when you're getting old). The school had historically done a "day of absence" where black students voluntarily absented themselves from campus, in order to demonstrate how valuable black people are to society as a means of addressing racism. One year, the black student club that organized the event went the other direction, and instead of voluntarily choosing to be absent, they instead required that white students weren't allowed on campus that day. One of the professors wrote a letter to the group and the school administrators, sharing the opinion that these two actions were not comparable - that there's a very real and meaningful difference between a person making a choice for themselves in order to make a point, versus a person making a demand of everyone else - that choosing to be absent is different from prohibiting other people to be present. That teacher was subjected to harassment, intimidation, and death threats until they quit in part because the school couldn't ensure their safety. Their opinion didn't deny anyone's rights.
At the end of the day, opinions cannot deny someone's rights. Hell, I could hold the opinion that you personally should not have the right to post on ISF. I can shout it from the rooftops, I can gather other people to take up the banner with me... but at no point would my opinion actually remove your right to post here. I have no authority over you.