I would be surprised if anyone thinks there is some kind of obligation to listen. As @FortyTwoV4pt2 points out, the First Amendment is to protect one's speech from the government. Perhaps a more interesting question is this: is the US government obligated to listen?

Here is another angle..... The Flat Earth dude have the right to say all that non sense. Do you want to give him the power to force you to listen?

You have the right to say whatever but, you don't have any guarantee anybody will listen. You cannot expect to have that power over someone else. See, I can say all this but it's up to you if you want to listen

Free Speech is the concept that government cannot proscribe expression, it does not include private individuals nor organizations. The question therefore answers itself.

Hard no. All the First Amendment guarantees is that the government cannot persecute you for protected speech. It doesn't protect you from people leaving you in the dust because you're an asshole.

Yeah, no. You have the right to not be imprisoned for your words. I have no obligation to listen or agree.

This smacks of dragging a horse to water and forcing it to drink at gunpoint..which wouldn't succeed anyway?
Unless you have a literally "Captive" audience nobody has the right to force people to listen to their opinion or ideas no matter how valid they are.

For example you may wish to patiently explain to a flat earther the error of their assumptions ..and having failed you may wish to shake them violently..but it would be futile anyway..? your arguments would be valid but it would be wrong to force them to listen or attack them. By all means ridicule them..

One extension of the freedom of speech, is that the court and police cannot force an individual to speak falsely.

Which raises serious concerns about the concept of plea bargaining.

You know what I think. It’s like your right to swing your fist ends at my nose.

Simplest answer: no. Your right to free speech does not change my right to ignore you. Furthermore, my right to free speech does not change your right to ignore me.

I have yet to meet anyone that thinks that.

Of course you don’t have to listen. Only time, manner and place can be regulated, not content.