I asked RMS about the GDB manual. It has two invariant sections, one of which is a "where to obtain GDB" section; the other is an introductory tutorial to using GDB. I asked RMS why the latter of these needed to be invariant. He replied that it shouldn't be invariant and he'll ask the relevant maintainer to fix it.
As for the former, I'm sure he intends that to remain invariant; it's not an accident. Still, the most egregious invariant section I know of has been fixed. :) I'm still cogitating about what I think the right thing is more generally, the arguments of many having been sufficient at least to give me serious pause.