I think people should be allowed to make political statements outside of a work context without risking their jobs—but with our current societal norms siding with corporate image concerns, this does seem in-line with the norms of that approach.

Define "political statement".

Because it looks like you're putting "this is just like beginning of the holocaust", "non-whites don't deserve human rights" and "let's seriously consider not having a secret police" in the same bracket here.

A statement being a political position doesn't (or rather shouldn't) automatically shield you from the other meanings of that statement and writing that off as all being "corporate image concerns" is insidious.