I believe the line is crossed when a person is willfully ignoring, or purposefully denying the evidence in favor of a feeling they own about a topic. I see this all the time. Those who espouse various conspiracy theories about NASA faking the moon landings, flat-earthers, alien abductions, etc. There are also many who are unable to accept the overwhelming evidence supporting the safety of vaccines, evolution, or any number of scientific theories and concepts. Their inability to accept the facts of the matter does not make "their opinion" acceptable, or correct, even if many others hold a similar "opinion". I could gather a hundred others and, with the aid of graphs showing the decline in number of pirates is proportional to the rise in global temperatures, convince them to join me in believing our current lack of pirates is responsible for global warming. That does not make us right. It is a misconception, or just plain wrong to connect those events.
For further reading, here are a couple of articles with much more in-depth coverage of the idea.