What does it mean to say "We are entitled to our opinion?"

When we say we are entitled to our opinion, what this means is that if we have a sincerely held belief, the powers of government don’t have the right to brainwash us and force us to change that belief. It doesn’t mean that we are morally justified in the way in which we hold our beliefs, nor does it mean that regardless of how rational or irrational our belief-forming processes are, our beliefs are as likely to be true as anyone else’s. We can have different opinions about whether our injured ankle is sprained or broken, but the well-informed judgment of a doctor is surely more worthy of consideration than the less-informed opinion of the patient or members of the patient’s family.