Being sensitive to harassment or offensive language directed towards them is not something which should be "dealt" with; it should be respected. No one has the right to just start slandering or harassing other players regardless of how low their skill level at the game is or how brain-dead their decision making is. That makes them a bad player; not a bad or defective human being that you have to "adjust" and accommodate them.
How about instead the person you are sympathizing with above learns to be respectful instead? It is your job to exhibit behavior which is not disrespectful or offensive regardless of the other player's level of sensitivity. Some will be "chill" about it while others will take offense. Your behavior should be such that it doesn't offend people of varying sensitive personalities.
I actually thought you were giving good advice to those who get frustrated while playing and get restrictions/bans when they retaliate in ways deemed inappropriate. I thought your post was meant to give healthy advice.
Now it seems to me while you may have suggested the proper approach for these people, your reasoning is very off. So muting is the right call to make b/c players themselves don't need to be careful in their behavior but b/c muting is a way to shut out sensitive people? The behavior of these people who are doing the harassing is pathetic not the sensitive nature of some/most players of the game.