What did Texas v. Johnson demonstrate about the right to disagreeable speech?

Unpopular opinions are protected under the first amendment and speech can not be limited based on its content

In 1984, Gregory Lee Johnson burned an American flag outside a convention center in Dallas, Texas, where the Republican National Convention was being celebrated. He did it as a way to protest the government and he was subsequently arrested and charged for his action, but he appealed and the Supreme Court heard his case. The majority of the Supreme Court agreed with him, arguing that burning the flag was an example of symbolic speech as protected by the First Amendment. This demonstrates that Johnson's right of free speech was recognized and respected.