No, students can't be kicked out of public school for refusing to stand during the Pledge of Allegiance

KHOU-TV (Matt Dougherty) reports:

India Landry, a Windfern High School senior, says she was in the principal's office on Monday when the pledge came over the intercom. She says the principal told her to stand, but she refused.

"And then the pledge came on, and they both stood, and then I didn't," Landry said. "[The principal] asked me to, and I said I wouldn't. And then she said 'Well, you're kicked out of here.' "

Landry's mother recorded a phone conversation which she said was with the principal (KHOU reports that the school district hasn't confirmed whether the person speaking was indeed the principal); and, though the school district has issued a statement saying, "A student will not be removed from campus for refusing to stand for the pledge,"

In the recording, the alleged principal clearly states that the reason for India's suspension is because she would not stand for the Pledge of Allegiance.

But W. Va. Board of Education v. Barnette (1943) concluded that the government—including public schools—can't require students to participate in the pledge:

[I]n connection with the pledges, the flag salute is a form of utterance. Symbolism is a primitive but effective way of communicating ideas. The use of an emblem or flag to symbolize some system, idea, institution, or personality, is a short cut from mind to mind. … Associated with many of these symbols are appropriate gestures of acceptance or respect: a salute, a bowed or bared head, a bended knee. …

[T]he compulsory flag salute and pledge requires affirmation of a belief and an attitude of mind. It is not clear whether the regulation contemplates that pupils forego any contrary convictions of their own and become unwilling converts to the prescribed ceremony or whether it will be acceptable if they simulate assent by words without belief and by a gesture barren of meaning. It is now a commonplace that censorship or suppression of expression of opinion is tolerated by our Constitution only when the expression presents a clear and present danger of action of a kind the State is empowered to prevent and punish. It would seem that involuntary affirmation could be commanded only on even more immediate and urgent grounds than silence. … To sustain the compulsory flag salute we are required to say that a Bill of Rights which guards the individual's right to speak his own mind, left it open to public authorities to compel him to utter what is not in his mind. …

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.

And while that case focused on the requirement that students say the Pledge of Allegiance and salute the flag, its logic applies just as much to requirements that people stand. See Lipp v. Morris (3d Cir. 1978) (en banc):

[The government] asserts that being required to stand while others engage in the flag salute ceremony is in no way a violation of the First … Amendment[, because] … mere standing does not rise to the level of "symbolic speech." … [But the precedents applying Barnette] interdict the state from requiring a student to engage in what amounts to implicit expression by standing at respectful attention while the flag salute is being administered and being participated in by other students.