Church/State Separation: Unconstitutional?

Does the 1st amendment to the US Constitution forbid handing out invitations to a Christian party at an elementary school? According to Fox News:

• A Pennsylvania elementary school…allegedly prohibited a student from inviting classmates to a church Christmas party…

• District policies, according to attorney ADF David Cortman, prohibit any student speech promoting Christianity. “It’s another example where schools need to be educated about the First Amendment,” Cortman told Fox News Radio. “The policies that are at the heart of this lawsuit are unconstitutional.”

Well, doesn’t the Constitution demand church/state separation? This is how the famous 1st Amendment reads:

• Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.

Although Congress can’t establish its own national religion, this doesn’t mandate a church/state separation. Furthermore, this in no way forbade the States from establishing their own State religions. In fact, God is mentioned in all 50 State Constitutions. Here’s a sampling:

• Massachusetts 1780: We...the people of Massachusetts, acknowledging with grateful hearts, the goodness of the Great Legislator of the Universe...in the course of His Providence, an opportunity and devoutly imploring His direction ...

• New Jersey 1844, Preamble. We, the people of the State of New Jersey, grateful to Almighty God for civil and religious liberty which He hath so long permitted us to enjoy, and looking to Him for a blessing on our endeavors.

• New Hampshire 1792, Part I. Art. I. Sec. V. Every individual has a natural and unalienable right to worship God according to the dictates of his own conscience.

• Vermont 1777, Preamble. Whereas all government ought to ... enable the individuals who compose it to enjoy their natural rights, and other blessings which the Author of Existence has bestowed on man ...

If God is mentioned in all of our State Constitutions, why can’t He be mentioned in our schools? Why has what has so clearly been constitutional, suddenly been deemed “unconstitutional?”