> If I'm not mistaken, BIP444 proposes having a council or group of people making decisions on what is "troublesome content".
I didn't see anything explicitly about a council. If the "group" is defined as the set of miners, then I think it would be wrong to assert that this proposal "gives" them power to make decisions on what is troublesome content.
On a related note, I think miners already have that power, implicitly, because they have a veto on what counts as valid in bitcoin. Specifically, even if all the non-mining bitcoin nodes consider some type of transaction valid, the set of miners can refuse to mine transactions of that type, thus effectively overriding the will of all other nodes.
I think it would probably be unwise to ask them to formalize this power in some sort of coordination software and then begin using that software to manually "vote" on what counts as troublesome content. (Again, i do not think bip444 proposes this.) A group with that kind of power in bitcoin sounds like a bad idea to me, and although I think miners technically have that power already, it is not, to my knowledge, formalized in any sort of coordination/voting software. If such software gets written and widely deployed among miners, I think bitcoin would be in greater danger than it currently is of becoming "ruled by committee."
Once more, I do not think bip444 proposes any such thing.
> And is the method of invalidating transactions to invalidate the entire block?
The proposed method is for miners to refuse to mine on top of any block containing a troublesome image. They would instead mine a replacement block without that image in it.
> what about all the other transactions in that block, what happens to them?
They go back into the mempool, to be mined in future blocks (presumably the very next one), except transactions such match the tx types identified in the bip, in which case those transactions would become invalid once this bip activates, either by the "emergency method" (which involves rolling back one block, and which sounds like a bad idea to me) or by the "flag day" method (which sounds like a decent idea to me).