It's not up to the base protocol. Nostr only sends signed messages back and for. If people want to create moderated chats, they can use those messages to build any moderation stack needed.

NIP-28, for instance, has some moderation capacities that clients may or may not follow. NIP-56 is about moderation via content flagging. NIP-36 is about self-moderation. DMs are basically a moderation tool for everyone but the two people talking to one another. The new scheme to only see the full content after paying an invoice is another moderation tool. NIP-82 for health data uses a per-message consent-to-see stack. These are all, technically, "moderation"

Relays have full moderation capacities because they can delete anything they don't like.