Relays that cater to a community (around a common interest, goal or group of people). 

To do that job well community admins can set whatever limits to reading/writing they like. 
Tools in their toolbox: 
- price lists
- white lists
- guidelines
- automation offered by their hosting solution (rate limiting, spam detection, ...) 

 For this it's important that the relay also let read and write for allowed people only.

Which relays software/code can currently do all of that? 

 For reading, unsure although perhaps strfry's policy plugin can do something?. But for writing you can whitelist npubs on strfry and nostr-rs-relay.