The justices did not divide on liberal/conservative lines in that case. "Conservative" Justice Antonin Scalia provided the fifth vote to overturn the statute. "Liberal" Justice John Paul Stevens was in the dissent.
Should the question be considered closed as a matter of respect for precedent (stare decisis)? Some of our friends on the left think that precedent is a ratchet. All precedents favoring their view are sacrosanct, while any precedents they disagree with are constantly subject to reexamination. Justice Thurgood Marshall sadly ended his tenure on the high court with one of the most hypocritical opinions I have ever seen, excoriating his colleagues for overturning a relatively minor (and, in my view, clearly wrong and unjust) Eighth Amendment precedent while Marshall himself had obstinately refused to accept a far more important (and clearly correct) Eighth Amendment precedent for 15 years.
On the merits, I think that flag burning has to be considered "protected speech" as long as we consider "speech" to extend beyond the literal meaning of the word into nonverbal expression. Anti-flag-burning statutes target content rather than "time, place, or manner." To authorize such statutes within a coherent body of free-speech jurisprudence, we would have to tear up far more than Johnson itself, and that is enough to let the sleeping dog lie.
Of course, we can and should exercise our own right of free speech to denounce the flag-burning scum in the most vigorous terms, but the government cannot punish them unless they violate some other, non-expression-directed law. Burning someone else's flag without permission is a crime. Burning a flag at a gas station ought to be a crime, if it isn't already.