Raising one’s voice when rebuking someone is not a sin, but rebellion is. See 1 Samuel 15:23, “For rebellion is as the sin of witchcraft.” You will not find a biblical comparison to loud vocal noises- “shouting is like witchcraft.”
Whether or not people respond well to a person raising their voice is a different matter. Though not a sin, it sometimes might be good (if the person is not being manipulative) to care for them as the weaker brother/sister and change your tone if they don’t respond well to loud voices. I suggest apologizing and moving on to the actual rebuke/correction. Once again, this is only if you feel it will help. Then you can test their heart to see if they are trying to control your rebuke by controlling your tone or truly wanting a different tone because of their weakness to loud noises.
Remember, don’t let the personal preference deter you from the rebuke- this is a tactic of deflection. Some insecure people believe that if they can get the “corrector” to start examining their rebuke they can take the attention away from their initial action which in fact deemed a rebuke. I call this “correcting the corrector.” Don’t fall for it- you are not subject to people’s immature feelings when they are in fact in sin, but we all are in fact subject to God’s Word.
You will not find one verse in the Bible that says raising the voice or what some people call “yelling” (in my house we called it “talking”) is evil or a sin. Gentle tones are just as good as bold tones when dealing with people- the situation determines the effectiveness.
1. IS SOMEONE IN WRATH & ANGER TOWARDS YOU? Try to calm them down with a gentle answer, Proverbs 15:1, “A gentle answer turns away wrath, but a harsh word stirs up anger.” Think of trying to calm down an intense argument that could lead to a fight (ex., road rage, etc.).
2. IS SOMEONE BEING DECEIVED AND ACTING STUBBORN? Try a strong rebuke- which would include raising one’s voice (Jesus’s culture was Middle Eastern, ever heard them talk? Reminds me of Italians!) Proverbs 27:5-6, “5 Better is open rebuke than hidden love. 6 Wounds from a friend can be trusted, but an enemy multiplies kisses.” Here even a wound to the pride can be helpful because it can shake them out of their own flesh.
It’s the same thing with name calling- depends on the situation. Get in the way of Jesus’s mission- get called Satan (just ask Peter). Mess with the prophets and get called prostitutes or even worse (I’ll keep it PG here but see Ezekiel 23:20 for more intense language). At the same time, Jesus was quick to speak words of life to those who came in humility. God favors the humble but opposes the proud (1 Peter 5:5). 
Gentle Jesus? See Jesus in the Temple the times He showed up with a whip. It may not have seemed gentle to those getting whipped, but it was still gentle because He used self-control. Jesus could have destroyed the entire temple with His breath.
So the next time someone wants to “tone police” you in a situation where their actions need strong correction or rebuke; remind them, “Raising one’s voice is not a sin, but rebellion is.”
Isaiah 58:1, “Shout it aloud, do not hold back. Raise your voice like a trumpet. Declare to my people their rebellion and to the descendants of Jacob their sins.”