Spouting quotes just makes you seem like a zealot and I suspect most people just nod and quietly assume it safe to ignore you.
Of course, there is also a risk that sometimes I am wrong. There are things that I believed to be true that were not, and I've gone back and told people so. Pursuing truth and being transparent about my mistakes and missteps builds trust.
People may not like me, and I'm fine with that. I would rather have their respect than their admiration. If they do not respect me, then I will do them the courtesy of keeping my opinions to myself. I don't waste my breath on cynics.
Appealing to authority can be a fallacious way to reason, however it can also be done correctly, and is a powerful way to influence people. I love your visual of phone/quote/mic drop - that'd definitely be the wrong way to do it :)