Philosopher Patrick Stokes has a go at claiming that we aren't. He says that it's a point he puts to his students every year: 'You are not entitled to your opinion. You are only entitled to what you can argue for.' Now, in truth, what Stokes is urging upon us is the thesis that some beliefs aren't rationally defensible, and he's right about this. He's not trying to suggest that matters of pure taste can be adjudicated right or wrong; rather, he's arguing against the idea that on questions where there is a truth of the matter all opinions are to be taken equally seriously. He gives examples of (what he takes to be) people challenging views for which there is sound scientific backing, and doing so on the basis of ignorant or frivolous objections. But he does allow that 'If "Everyone's entitled to their opinion" just means no-one has the right to stop people thinking and saying whatever they want, then the statement is true, but fairly trivial.'
Not only is it not trivial - it is of fundamental importance both morally and politically (for well-established reasons which I won't go into here) - but I think that Stokes's way of expressing his correctly anti-relativist view is misguided. Surely one of the main reasons for saying that everyone's entitled to their opinion is to insist on the point that they have a right that is unaffected by the quality of that opinion, good or bad or some combination of the two, right or wrong or in-between. To say that one is only entitled to an opinion of a particular status, e.g. to what one can (successfully) argue for, rather erodes the value of the principle. One's entitlement must be to any opinion one sees fit to hold or to proffer, even though there is no right to have one's opinion taken seriously if it doesn't merit that.
In the context of a philosophy class, too, I think one's entitlement to one's opinion, whatever it is, applies. Stokes would doubtless reject the truth of the opinion that all opinions are equally good. But I can't see any possible objection to its being defended, and even believed, by a student of philosophy, though I would hope she could be persuaded of its falsity. Similarly with the opinion, 'Many people disagree with the claim that P, therefore P can't be true'.
People are entitled to believe the most preposterous lies without this entailing that we must give credence to those lies. Reversing the logic, we can uphold our right to discriminate between good and bad opinions without impugning people's entitlement to believe what they will.