You can block nasty people on Mastodon at a personal level, by clicking the "..." below their post or on their profile and selecting "Block". You can also block their entire server by selecting "Block domain".
However, personal blocks will not stop them from communicating with other people on your server.
Your server's admin can create server level blocks, which are much more powerful than personal blocks. Server level blocks completely prevent the blocked person communicating with anyone on your server.
If you see someone being a bully or doing other anti-social and nasty stuff, the best option might be to report them to your server's admin, by clicking "Report..." instead of "Block...". Reports can also be optionally forwarded anonymously to the nasty person's home server, where the admin can delete the nasty account if needed.
Server-level blocks can be made even more effective if your admin activates "Authorized fetch" (also known as "Secure mode"). Ask them about it.
@feditips
If you block them for yourself, why would you care if other people decide to not block them. To me, personal level blocks are the way to go. If you don't want to see what someone posts, you shouldn't have to, but at the same time, it really shouldn't be any of your business if someone else wants to view said posts.
@feditips
It seems to me that the people telling other people who they can and can't listen to are the ones being the bullies.
There are thousands of servers on the Fediverse, if you don't like the rules on one of them join a different server or start your own.
That's the way the Fedi works, each server decides for itself what is acceptable, and people can move to the server that suits them.
You're free to do what you want, but so are other people. I only join servers that block bullies, but you don't have to.
@feditips
I am on a server with rules that I like.
1. Don't post anything illegal.
2. Don't harass others.
Simple, easy to enforce. The have also set it so that there is no server tab so that you only see posts from people that you follow. That way it is very easy to self moderate.
If I wanted server admins to tell me what I can and can't see or say, I would join twitter.
@jlcrawf
"why would you care if other people decide to not block them."
...because bullies aren't welcome here, or at least not on any server I would join.
It's everyone's business if someone is doing something nasty or hateful.