Should his freedoms be stifled just because he's famous?
No, because he represents a larger idea than himself.
Just because he's achieved more than most of the rest of us could even dream of?
No (assuming that's true), but because what he's achieved is precious and valuable and shouldn't be destroyed. And the achievements built by the hundreds of GNU maintainers are also precious and valuable and are worthy of protection.
His opinions on some things are invalid just because he's well know for his opinions on other things and people look up to him?
Not at all, but because sharing his opinions on controversial matters (valid or invalid doesn't matter) unrelated to Free Software risks the stated goal of GNU to empower all computer users.
It's not tall-poppy syndrome, it's a unfettered free-speech sacrifice public figures can make to further their other goals (in this case, GNU). There are more qualified people than RMS to speak out on correct usage, legal terminology and the psychological harms of abuse. His silence on these topics is no loss to the commonweal when set against the potential harm to the GNU project, and others will surely make those arguments if needs be.
Obviously if RMS were not the figurehead of GNU (or until recently FSF) I'd absolutely agree with his speaking freely on any subject and I'd agree with your first para "I don't agree with ... regardless of his position." without qualification.
I've found honesty is, rather strangely to you perhaps, the greatest basis for trust.
I don't find it strange at all. But a simple evaluation of honesty in the moment of a conversation or other transaction is not always possible. To return to the psychology aspect, we use courtesy, respect and adherence to norms as a short-hand if imperfect way to judge the trustworthiness of otherwise unknown persons to us, where we cannot independently check the honesty of that person or their statements. It happens all the time, subconciously. You might be rationally evaluating their honesty, but under the hood, you're absorbing the messages from their conduct. You could be misled if they can fake it, but that's not your fault.