That has little to do with your original question, which is "why do people get so agitated?" The answer remains: I haven't seen people get any more "agitated" about it than about any other form of bad writing, and headhopping is bad writing when it makes a book hard to read.
"...if it can be got right..." is the critical part. Like the use of present tense, it very rarely is.
Switching POV is no more or less important for that group of characters in debate than any other stylistic choice is. As a counter-example, if you stay with a single POV, you can show your main character being overwhelmed by the people all proclaiming their opinions. It might work better, in fact, in creating that sense of urgency and confusion than if you were to switch POVs so that every character could mentally explain his opinion instead of just shouting it.
"Hang him high!" the skinny cowboy shouted.
"Hanging's too good for him. Drown him!" said the drifter in the corner.
"No, no, that's not right, my good people," said the preacher. "We must show him the error of his ways." That brought a few guffaws.
"String him up!"
"Tear him apart!"
Sally was starting to get a headache. It wasn't her fault that the fool had chosen to do his drinking in the Last Chance Saloon, but somehow she was caught in the middle when he got soused enough to tell bad puns.
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