I just made a discussion about my experience with the report system. My top laner was being toxic and everyone muted him. Then I got a comment saying that I was in the wrong for doing so and I ruined his experience. If I'm a bad person for muting people then why would Riot have it in the game. Lastly, what do you use the mute button for? I use it to ignore people flaming.
Personally I almost never mute people, but there is nothing wrong with doing so. I would rather have communication open since even a broken clock is right twice a day.
Mute people as you see fit.
Ignore them. If they are toxic then you need to mute and report them.
Did you tell him you were muting him? Were you rude at all.
Muting people is perfectly fine as long as you continue to communicate with pings. The mute button is there so that if someone is being toxic, it doesn't further ruin your experience. You will never get punished for simply muting a teammate unless you were being toxic yourself.
When I mute someone, they've crossed my 'report line' and the muting helps remind me of that at the end of the game.
Mute everyone every game if you want to avoid getting reported. I just got over a chat restriction and I made post about this called Chat Restriction Bias if you want more information.
