An article I read recently put it well that everybody was entitled to their informed opinion. If somebody doesn't even take the time to think up a reason at the very least or ignore facts they shouldn't expect people to respect their half-assed opinion. Like I don't feel entitled to an opinion on which car part is best because I have no idea. Like how people have opinions on science when they really have no idea what they're talking about. And of course opinion can be about things like which ice cream flavor they prefer which is just about personal preference.
That sounds reasonable. However, I'm not sure if you can deny people their right for an opinion by saying "you're not entitled to your opinion if it's not informed". Of course they are! - we are. It's just how human beings are; right for opinion next to right to think for oneself. That being said, it sounds unreasonable to respect all kinds of opinions: not every one of them is well-informed, therefore implying and/or entailing nothing but bias and conformity - and there's nothing respectful in either of those. Think ill of others all you want - but as long as you have little or no basis for it, don't expect me to respect that. "Niggas oughta be killed" is... no. Go fuck yourself; no. On the other hand, "Pseudointellectuals who display their phony education and understanding of the world are bad to listen to and stand in vicinity of in general because they confuse others with unbased confidence in a field they barely understand, thus leading to a more closed-off and excessively self-confident mind" and so on... I can get around to that.
When people say they are entitled to their opinion it's generally because they are being dismissed. In that context it seems that what they mean is everybody is entitled to their opinion being heard. As if you can't tell somebody they are being ridiculous because hey they are entitled to their opinion. That's generally what people are diagareeing with when they say no you aren't entitled to an opinion.