I am thinking of banning depressed people from a streamer's twitch chat.
Do you have a reason to ban them from the chat?
I hate people who are depressed since they prey on my stream.
You are being mean excluding people from the chat. It is expected that sometimes certain people will struggle with depression. You should set some rules for the chat but not exclude people because of their illness.
I'm a mod and only I can decide who I ban from the chat
That is true that you have the authority to mod your chat as you like. However, if the other chatters notice you banning people for no good reason, they might not stick around to watch you. You should help them to cheer up by entertaining or asking them what is wrong.