Okay, this is a good argument, save that this premise is wrong. The word "right" is used to mean things that are not or cannot be enforced legally, and when used as "moral right", outside of copyright law where moral rights have a specific technical legal meaning, is not identical to legal rights or the desire to actually implement a corresponding legal right.

For example, you have a legal right--as long as you're not under contract or making statements of fact about a product you're delivery--to lie to enrich yourself at the expensive of those who are poorer than you. This is not, however, a moral right. And because of the difficulty in adjudicating what is a lie and what is a difference of perspective, it's unlikely that this will or should be brought closer to the moral ideal. We have found ways to legally constrain some of the most egregious violations in areas that are particularly detrimental to society, but every legal intervention has downsides (often impinging on other moral or legal rights), so it's hard to see how much farther we could go to align moral and legal rights in this regard. But when we detect the immoral action, we certainly can criticize and judge them as a social matter.

In contrast, you have a moral right as a child to grow up in a safe home. But you don't have a legal right to grow up in a safe home--only to avoid really egregious abuses of safety. Again, because of the blunt nature of the law, the downsides of intrusions to verify home safety, and so on, it's implausible that the legal and moral rights can align here. But we can advocate in our society for the virtues of having children be safe at home, so people will self-monitor far beyond what is practical to enforce legally.

It is in this sense (which is well-established; Google isn't helpful because "moral right" has a legal definition in copyright which confounds search results, but ChatGPT and Bard know what's up) that I mean "moral right". For more background on the concept of rights as a whole (and I mean them in this sense), see Wikipedia: https://en.wikipedia.org/wiki/Rights

In particular, you do not have a moral right to immoral behavior. By framing education and rationality as virtues, Locke, Rousseau, and contemporaries place proper mental conduct as a matter of morality (from a virtue ethics standpoint). This is why I'm completely comfortable with using them to support the idea that certain types of intellectual sloth and carelessness can in fact be immoral, and as such, one does not have a moral right to conduct oneself thusly.

However, it does not follow that I advocate for that type of immoral action to receive legal sanction in all but the most dire of circumstances. The reason is the same that we often have a disparity between what we view as moral and what we enshrine as legal: it is often neither possible to detect or enforce, and the cure is often far worse than the disease.

So I simultaneously hold that (1) people do not have a moral right to carelessly acquired and poorly-examined beliefs, especially if those beliefs are of the sort that tend to impel actions that harm others, but also (2) we should not restrict their legal rights to belief or expression thereof because it is ineffective and will do more harm than good (indeed, being able to express the beliefs is part of the intellectual due diligence they need to get back onto morally solid ground!).

Thus, when you say, "No person has the right to question someone's beliefs." I completely disagree--not only do we not have the right, we actually have a minor obligation to question each others' beliefs, and stay alert for signs that questioning might be necessary. This doesn't mean social media pile-on cancellation; that isn't "questioning", that's "shunning".

Anyway, I think I'm very nearly in agreement with Rousseau, and quite close to Locke too, here. The main quarrel I have with both of them is that I think that the framing in terms of rights is mistaken. (I actually wrote an article on this: https://medium.com/@ichoran/responsibilities-are-more-fundamental-than-rights-69c80413d638.) But as long as you interpret my meaning correctly, and discern the difference between moral and legal rights, I think my outlook as descibed here is far closer to that enshrined in the U.S. Constitution and the thought that prompted it than yours is.