TL;DR
Empathy goes a long way. Politeness goes even further, and biting your tongue takes you all the way home. (Also snacks. Deathtimers get long, so if I’m stuffing my face with something, I can’t type.)
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I’ve never muted chat, I try to restrict my use of it to gameplay decisions (not quality of the play unless it’s a gj or thanks for example) and I’ve never had a chat or other ban.
I do get frustrated, but generally it’s with my game play. Sometimes I get annoyed that we have a player who really can’t play their role, and I know I’m not going to get a win regardless of my play, but I’ve never tilted over it.
One thing I try to remember is that at my ELO, it’s not inconceivable that there are players on my team in the same boat as me - they consistently get MVP, A or higher in normal and are now trying ranked and kinda suck. I genuinely have no idea what I’m doing wrong (positioning is one thing I do know I need to work on). This is especially true of junglers, I think. Jungling is hard, which is why I never play it in any mode, unless forced too. So asking myself if I could do any better, and realizing that ‘no I couldn’t’, keeps me from piling on to the poor guy currently shouldering the blame or the guy who's lashing out. So that’s part of why I don’t flame.
As far as not reacting to flamers, I call upon my innate Canadianness and apologize. Then I ask ‘what would you like me to do, cause I really want to support you?’. Sometimes, there is nothing I can do - the ADC is being too aggressive early lane, not watching wards or thinks hanging around lane against ranged opponents at 50 health with both summoners blown is a good idea and so I get flamed. I get it, and responding will just make them tilt harder cause now they have an audience and outlet so it’s better for their gameplay to for me to shrug it off. The closest I get to salty is saying, ‘moar winning, less typing’ but it has to be really bad for me to hit button 12. Once in a great while, I’ll stoop to a, “I liked it better when you were being constructive.” (Mostly in games where nothing constructive was said.)
I had a really interesting experience with a Master Yasuo last night that reminded me that not all flamers are actually jerks - they sometimes don’t understand other roles. I was throwing a ward into brush (I was slightly behind him) and died in the ensuing fight with the revealed enemies instead of cutting and running, I got one kill. Yasuo lived, got a kill and was like wtf Neeko when he died escaping and ran into another player. I replied, I was helping You. (It's my job to die instead of him, helping him escape was my goal). A minute later, he was like, you’re right, I apologize. I said thank you, and added that I wished I was better at helping. I didn’t bother to point out that he face checked - there was nothing to be gained. He knew.
There’s probably not much helpful advice buried in that text wall. I did put a TL; DR though.