Yes, and some opinions happen to be plain wrong, and others are similarly entitled to say so. The entitlement to state an opinion does not guarantee its correctness.

Ok, I guess that joke was a little bit too subtle.

Let me rephrase that reply: Everyone is entitled to his own opinion.

Everyone takes the singular, but in that reply, I paired it with the plural their.

Yes, and everyone missed the joke because that sentence reads naturally, thus proving that "their" is an appropriate pronoun to use.