I've personally never felt the need to mute words or people on Twitter or any other social network. I follow 540 accounts on Twitter right now and disagree with most of the political perspectives espoused therein. Yet I don't mind seeing any of this sort of thing on my social media timelines for a couple reasons.
For one, if I were to mute opinions that I disagreed with, I feel like I would be in effect turning a blind eye to the fact that people have these opinions. I don't see any value in this; people all over the world have all sorts of different opinions, and deluding myself into believing that people who disagree with me effectively don't exist seems... wrong, morally, at least to me. I specifically follow individuals (both public figures and not) whose opinions (political and otherwise) don't align with my own. I _want_ to see thoughts that aren't just identical to the ones already floating around in my head!
Also, I personally believe that associating emotions with words and phrases in the minds of the populace so strongly as to cause one to either react with outrage or reach for a digital mute/hide button, is one of the strongest weapons of social destruction today. This is a means of socially engineering people's reactions to specific ideas, conditioning them on a mass scale to be unable to use logic and reason as their emotions short-circuit any such thinking. Since mid-2016 I have gone to great lengths to refrain from becoming "outraged" by outrage-bait news and social media posts, and I've found that it's increased my personal happiness and outlook on life considerably, especially as the mass and social media ramp up their production of nigh-constant outrage fuel, and everyone seems to want to make _everything_ political.
Who said anything about disagreements, much less outrage, though? The context was cutting out noise, and muting is a more effective version of skipping your eyes past it. Some topics just get spent and become boring.
The article was basically about this ("So I began to take note each time I experienced a little hit of outrage or condescension or envy during a Twitter session. What I found was that nearly every time I felt one of these negative emotions, it was triggered by a retweet."), and in my experience this is largely how the "mute" functionality is used: literally to protect yourself from experiencing the learned emotional trigger associated with seeing specific keywords or phrases.
Fair enough, but this subthread had diverged to a discussion of the logistics of reading a large number of feeds, and the mute functionality was suggested in that context.