There is no 'war on Christmas,' the notion is ignorant rightwing idiocy and a lie.
Establishment Clause jurisprudence requires that government involvement in religion have a clear secular purpose, that the primary goal of government must not seek to advance religion, and that government must not become excessively entangled in religion. (
Lemon v. Kurtzman)
'Noting that the city’s name is Spanish for Bethlehem — hence the display — the mayor pointed out that locals have strong feelings for the display, and that the city will go as “as far as we can” legally to keep from having to move it onto private property.'
To be in compliance with the First Amendment the town should remove the display, as it has no secular purpose, as it serves solely to promote religious advocacy:
“When viewed in its overall context, the creche display violates the Establishment Clause. The creche angel's words endorse a patently Christian message: Glory to God for the birth of Jesus Christ. Moreover, in contrast to
Lynch, nothing in the creche's setting detracts from that message. Although the government may acknowledge Christmas as a cultural phenomenon, it may not observe it as a Christian holy day by suggesting that people praise God for the birth of Jesus.
[...]
The Constitution mandates that the government remain secular, rather than affiliating itself with religious beliefs or institutions, precisely in order to avoid discriminating against citizens on the basis of their religious faiths. Thus, the claim that prohibiting government from celebrating Christmas as a religious holiday discriminates against [492 U.S. 573, 575] Christians in favor of nonadherents must fail, since it contradicts the fundamental premise of the Establishment Clause itself.”
ALLEGHENY COUNTY v. GREATER PITTSBURGH ACLU FindLaw