But who actually has the authority to "moderate" a decentralized/censorship-resistant network?
Miners always moderated it. If you have "Alice -> Bob" transaction, and "Alice -> Charlie" transaction, then miners decide, which one should be confirmed.
Also, nodes always moderated it, by enforcing "standardness rules", which also allows upgrading the protocol, without blocking anyone else's coins. When standardness rules will be lifted, then it will be harder to upgrade the protocol.
OR, who gave those people that try to "moderate" it the authority?
They have the authority, because they have a lot of hashrate, so they can produce a lot of Proof of Work. However, if users will be disappointed, then they can always pick a different chain as "valid", and move their coins to the system, which they want to use. And for that reason, miners can decide about a lot of things, but not about everything.
And when it comes to nodes, they can always moderate the traffic. More than that: they can provide different services. There are nodes, which don't relay any transactions at all, but they are still part of the network, because they accept blocks.
Any node can decide, which features are supported, and which are not. For example: P2P marketplace was supported in the past, but it was disabled in early release. The same with poker game, built into the client.
Plus most importantly, is the "moderation" actually working/is it actually effective?
Yes, because if your transaction is mined by a pool with 1% hashrate, and censored by 99% of hashrate majority, then on average, you will wait at least 100 blocks, to see it confirmed.
Also, it is possible to accept a lot of transactions in relay mode, but include only a small subset of that in produced block templates. Because relay rules, and block creation rules, are separated.
It would be stupid to support such a move if it isn't, no?
I think relay rules will be more relaxed, and maybe even non-standard transactions will be relayed in the future. But block inclusion rules should be more strict. Because then, users could send a lot of things over P2P network, and a lot of these things can be used only for communication, related to making batched transactions. And then, users could send hundreds, or even thousands of transactions, and all of them could be relayed. Then, all of that traffic could be collected and processed by nodes. And then, the final, batched version, with the highest fees, could be taken by miners, and confirmed.
Also, P2P batching is actually used in practice, for example in signet faucets:
https://mempool.space/signet/tx/2f4ffd821a1d81f27cc2b16c50c7105e8b25585fd0a68a80c70da35a62b99107See "RBF Timeline", where the same transaction is bumped over and over again, until it is confirmed. In the same way, users could start sending transactions, and bump them by single satoshis each, and finally, it could reach 0.1 sat/vB, 1 sat/vB, 10 sat/vB, or any other meaningful fee rate, and serve many users, while also taking less on-chain bytes, than it would, if people would send it without any batching.