(Illegal in many countries post the rise of social democracy, for what it’s worth—the US being a notable exception.)

Not really true for Germany during the cold war, pretty sure that wasn't the only example. Just think about things like security clearances.

France specifically lists political affiliation among protected categories, while post-socialist countries flat out prohibit hiring decisions on anything unrelated to the ability to perform the job (and arguing “cultural fit” qualifies would be a difficult proposition, were the rejected hire to actually go to court).

Governments may be allowed to be more discriminatory for national security reasons, and AFAICT security clearances are in part a backdoor to get this to be permissible in private employment as well.

(Of course, it’s a different story if the political organization in question is actually banned, but in most civilized places that’s a very high bar—I’d argue that’s one of the qualifications of the moniker, even.)

Not to forget: Government is also a large employer, not just the private sector.