I disagree with you, Kuhn expressed that he believes that a leader pushing a controversial message unrelated to an organization’s purpose can become a distraction which has consequences, whether you agree with the leader’s controversial message or not.
That is not invalidated by the fact that Kuhn also disagreed with the views RMS has expressed and Kuhn clearly wished to distance himself from those views.
"Give the game away" is too strong, you're right. I don't mean to imply that Kuhn didn't mean what he carefully wrote, he seems like a standup guy doing Free Software.
It is possible that there are multiple angles and reasons why a leader is no longer compatible, and that there is no 'game' to give away.
EDIT: What I mean is, it's entirely possible that its not just that Stallman had views that were disagreeable, nor that Stallman wouldn't stop talking about his personal views- its that Stallman wouldn't stop talking about his specifically disagreeable personal viewpoints.
Absolutely possible and I don't have a hard time believing they'd reached that point with RMS.
I hadn't seen RMS's politics link before -- he puts out like 10 bullet-point hot takes a day, lots of them with a viewpoint way outside the mainstream. He's got weirdo semanticist takes about basically everything, including, as infamously linked, sex laws.
I normally want to defend the right to have unorthodox takes on general principle, but I can see where they're coming from here as far as leadership.
If you're gonna go with that line, stay on-message.