This flowchart, from an atheist group, is overly specific to their subject but, for me, a good guideline.
If your "opinion" isn't open to this kind of debate, it isn't an opinion, but a religious belief or an article of faith. Which get treated quite differently than opinions. You change an opinion with data. You change faith with emotional experience.
My own position is that "not judging" is an utter crock, in the sense that we always judge in reality, it's just a fundamental mechanism that human minds use, and not judging is as unlikely a phenomenon as not thinking - and I mean the whole mind not thinking, not the meditation technique of quieting your self-reflective mind to hear the other stuff. The other stuff is thinking too, and it ALL has to shut up before you can say you're not thinking (i.e. in a coma, not even hallucinating or dreaming). Likewise, not to judge would be not to discriminate - by ANY criteria. Not race, or gender, but live/dead, friend/stranger, employee/customer - ALL of these are forms of discrimination - people are treated differently based on what category they belong to.
The trick with judging is to not imagine your judgments to have any more significance or scope than they do. If someone's religion is fucked, that's one person, not one religion. If one nation's worth of religious people is fucked, that's one nation, not the whole world. If yo like or dislike something, you are you, and not a representative of a demographic. The royal "we" has no place in your judgments, nor does the "is of identity".
OF COURSE people don't all have the right to believe what they want. Airplane pilots do not have the right to believe in the flat earth theory, while taxi drivers do. Geologists do not have the right to reject plate tectonics, while plastics engineers do. Police officers do not have the right to believe in child abuse as a control technique, but ministers do.