You might receive a couple of different answers. "Everyone is entitled to his opinion" would be correct, as is your own suggestion. You could also simply say "Everyone is entitled to an opinion."
For those of us who subscribe to a more descriptive view of the language, "their" might considered correct in that it is used as a replacement for the more inclusive but more awkward version: "Everyone is entitled to his or her opinion." Note that textbooks and teachers will likely disagree with this!