Patently unconstitutional if actually made mandatory. At least until the courts tear up an 80 year old venerated precedent. Justice Jackson's opinion for the Court put it best:
"The case is made difficult not because the principles of its decision are obscure but because the flag involved is our own. Nevertheless, we apply the limitations of the Constitution with no fear that freedom to be intellectually and spiritually diverse or even contrary will disintegrate the social organization. To believe that patriotism will not flourish if patriotic ceremonies are voluntary and spontaneous instead of a compulsory routine is to make an unflattering estimate of the appeal of our institutions to free minds. We can have intellectual individualism and the rich cultural diversities that we owe to exceptional minds only at the price of occasional eccentricity and abnormal attitudes. When they are so harmless to others or to the State as those we deal with here, the price is not too great. But freedom to differ is not limited to things that do not matter much. That would be a mere shadow of freedom. The test of its substance is the right to differ as to things that touch the heart of the existing order.
If there is any fixed star in our constitutional constellation, it is that no official, high or petty, can prescribe what shall be orthodox in politics, nationalism, religion, or other matters of opinion or force citizens to confess by word or act their faith therein. If there are any circumstances which permit an exception, they do not now occur to us.
We think the action of the local authorities in compelling the flag salute and pledge transcends constitutional limitations on their power and invades the sphere of intellect and spirit which it is the purpose of the First Amendment to our Constitution to reserve from all official control."
West Virginia Bd. of Ed. v. Barnette, 319 US 624 (1943).