Are they? They are objecting Musk posting provably wrong statements on social media, arguing that as a fellow of the RS he shouldn't do that - the statements are on a variety of topics, not just Fauci.

Let's take your word for it. Fauci is a fellow too. If they are so concerned about spreading truth, why don't they object to his provably false statements and unethical exclusion of NIH funding of scientists (proof in email records) he does not like and ask for his exclusion?

You very well know the answer to that.