Majority Holding (5-4)

a.    Yes.  Brennan, who wrote the majority opinion, held that D’s
conduct was symbolic, and thus he was able to make a First Am.
challenge.
b.    The Court then proceeded to analyze the two separate
objectives that Texas asserted it trying to achieve with the statue:  (1) preventing breaches of the peace; and (2) preserving the flag as a symbol of
nationhood and national unity.
1.  Note that the Court here looked at the purpose of the law—not the
motives behind the law—and in this sense this case is consistent
O’Brien (where the Ct. discussed the purpose of the law—efficiency of
running the draft—but refused to get involve in the hippies-burning-cards-as-a-protest” motive behind the law.
As to objective (1), the majority simply disbelieved that preventing
breaches of the peace was what had motivated Texas on these facts
(since no disturbance of the peace either actually occurred or was
threatened by this particular flag burning).  Specifically, the Court
held that the potential for disturbance, or even violence, would be
insufficient under the two-prong Brandenberg test, and the “fighting
words” doctrine also did not apply because “no reasonable onlooker
would have regarded Johnson’s generalized expression of
dissatisfaction with U.S. policies as a direct personal insult or an
invitation to exchange fisticuffs.”  Besides, TX already had a
statute to deal with breaches of the peace, which suggested that the
“flag burning” statute did not punish flag desecration in order to
keep the peace.
2.  This seems a little disingenuous.  Of course burning a flag could
have a strong tendency to inflict injury or lead to a breach of peace
under the ‘fighting words” doctrine.  What if the onlookers were
veterans, which may have been very possible?
As to objective (2), the Court—unlike with breach of peace—finds that
protecting the flag as a symbol of national unity is a valid state
interest.  The Court then applied the O’Brien test, which the Texas
statute failed.  Why?  Because under the third part of the four-part
O’Brien test—that [the state] interest was unrelated to the suppression of free expression—the Court held that the TX statute was not content-neutral.  Specifically, the Court held that the statute was content-based because it was not aimed at protecting the physical integrity of the flag in all circumstances, but only at protecting the flag against mistreatment giving serious offense to others.  “If he had burned the flag as a means of disposing of it because it was
dirty or torn, he would have not been convicted of flag desecration,”
but he would be convicted if he burned the flag and “caused serious
offense to others.”  Because the statute was “content-based,” strict
scrutiny thus applies.  The Court then wrote, “If there is a bedrock
principle underlying the First Amendment, it is that the Government may not prohibit the expression of an idea simply  because society finds the idea itself offensive or disagreeable.”
Here, Texas’s objective—preserving the flag as a symbol of national
unity— may have been worthy, even “compelling.” But the means chosen
by Texas to serve that objective were not necessary ones. First, the
majority didn’t believe that the nation’s belief in the cherished
significance of the flag would be undermined by acts of mutilation;
indeed, these acts might produce the opposite result. Second, the
government could combat such acts by acts of its own, such as giving
the remains of the flag a respectful burial (as one witness to  Johnson’s burning did).