Is everything accepted as a BIP these days?
Maybe not "everything", but definitely a lot:
Stumbled upon this ... I wonder how this got accepted as a BIP? Wasn't there a quite length-ish process for BIPs to be accepted which had to be fulfilled by the proposers?
No, the process was always essentially to publish virtually anything so long as the proposers applied with some relatively trivial formalities and there are plenty of pretty awful bips. But for a long time Luke-jr was the only person doing anything and he'd just sit on stuff forever, so that did rate limit it. More recently there are new editors who are no longer letting things languish and have also leaned into the original principal of being generally permissive. But still even the simplest of formalities still stops a lot of people.
Hopefully some of the harm of crappy bips will be mitigated by more crappy bips, and will help shake people out of believing that because there is a bip number assigned that it's something anyone should implement.
Who's in charge of the BIP repository?
If you assume, that every BIP should be implemented, then you are wrong. Basically, BIPs are just used for standardizing things. They only reflect the point of view of the authors. And they are used just for coordinating things, like "I, as the author, want to do X, if you agree, then you can implement it in a compatible way". In decentralized consensus, it is mainly needed, just to group similar ideas together: because for example if you implement Silent Payments differently than in
BIP-352, then you could end up with people, sending coins to each other, which wouldn't be visible by the second party, if the scanning would be completely different.
And similarly, for quantum proposals, it should be more or less clear, what people are going to support: if they accept freezing coins or not. If they want to block some things permanently, and make them recoverable only with a hard-fork, or if they will just put a huge locktime, and make them movable later in a backward-compatible way. And for things like that, it doesn't really matter, which algorithm would you pick: the decision to freeze or not to freeze, is the same in all cases. Currently, I don't see the case, where someone would want to freeze coins for "foobar" signatures, but not freeze them for "barbaz" signatures.
I originally thought it was limited to P2PK and other public-key revealing scripts.
No. Every time, when you have OP_CHECKSIG, or its equivalent, then it is applicable. The whole Lightning Network works on public keys.
Almost nobody's coins would be unsafe (with the exception of P2PK/P2MS/P2TR keyspend and reused addresses)
I don't know why people think, that breaking secp256k1 with 128-bit security would be faster, than reaching RIPEMD-160 collisions, where they have 80-bit security against collisions.
What will cause a bigger FUD: a theoretical quantum computer, which could break random public keys in theory, or a real classical computer, which could spend coins from the same 160-bit address in two or more different ways?