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

Explanation:

It wasn't exactly disagreeable speech. The Supreme Court wrangled about the place of the American Flag in American life.

The core issue was whether or not desecration of the US flag is protected by the First Amendment.  The Supreme Court's final decision was yes but only by a 5-4 margin.

So in effect disagreeable speech was upheld. Various attempts have been made to make burning of the flag just going a bit too far. All attempts have failed and the right to disagreeable speech has been upheld.