No, you're imagining complications that don't exist. The very boring answer is that if two people (or groups) want to exercise their right to free speech at the same time, the government is charged with fairly apportioning the space to each of them in turn, in such a manner that both will ultimately be able to express themselves. If one of the parties feels the government is unfairly restricting their right to speech, they can take the government to court, and the court will adjudicate the dispute.

What people are describing as "cancel culture" is a totally different phenomenon.