This is an incredibly important point.

A gentle tone can make a discussion more inviting to participate in, but possibly at the expense of even being able to tell what isn't agreed upon. With a harsh tone, clarity about disagreement is rarely an issue and the tone also can be used as a credible demonstration of strength of belief for one position in an argument, which is relevant when deciding where to focus effort (you'd better bring your A-game if someone feels very strongly).

Either way, the tone is irrelevant to the correctness; it just might facilitate (or obfuscate, or derail) the conversation.

We (internet users especially) would get a lot more out of speaking at each other if we embraced what tone could do for us, either way, and focused more on the correctness of the thinking.