Not all opinions are as rationally based or as grounded in reality as others, but I take every opinion seriously, and I take the 'stupid/wrong' ones (as of the example you gave) more seriously as they are indicative of the mindset of the individual or a group in society, or a society itself, or even humanity. The 'right' opinion is usually less interesting to me as it is based in fact and there's not much to discover beyond the fact itself, but the 'wrong' opinion could be based on psychology, past experience, common misconception, a sociological factor, a meme etc etc. That's why I give 'wrong/invalid' opinions the same, or more attention.
Yeah, the "wrong" opinion are more interesting because it can help you understand that person's way of thinking and POVs which can help you determine whether you can convince them how wrong they are, or not.
However there is a certain point indeed where you have to call that person an IDIOT provided that person is very stubborn and arrogant like Clawed.
IRL, i hardly argue mostly because of the fallacies such as strawman arguments instead i try to understand why they stated that particular opinion like my neighbour who thinks that women shouldnt be working because he believes they are naturally born to be mothers and housewives plus being career woman means "whoring". Now i cant engage myself in this argument because no matter what, at the end the argument will lead to religion which would be more frustrating. Just like tonyt said
"Everyone should be permitted to express their opinion. But noone should be forced to respect any opinion".