Final answer:
A 'Happy Holidays' sign in class would generally be acceptable under the Establishment Clause since it doesn't favor one religion over another or religion over non-religion, and is considered a neutral greeting. However, anything more explicit could be subject to scrutiny.
Step-by-step explanation:
According to the Establishment Clause, displaying a "Happy Holidays" sign in class would typically be viewed as constitutional as it does not favor one set of religious beliefs over another or favor religion over non-religion. The courts tend to allow for a degree of ceremonial deism, which acknowledges general religious sentiment without specific religious content.
Signs that say "Happy Holidays" can be interpreted as a neutral greeting that is used enthusiastically by non-Christians and even in non-Christian nations, and it tends not to be specific to any one holiday or religion. This differs from school-sponsored prayer or bible reading, which the Supreme Court has deemed unconstitutional in public schools, as highlighted in Santa Fe Independent School District v. Doe and Abington School District v. Schempp.
Nonetheless, if the display were to lean towards a particular religious holiday or became more explicit in religious tones, it might then be subject to scrutiny under the Establishment Clause, as it could be seen as the government favoring one religion over others or religion over non-religion. In general, the Establishment Clause ensures that the government does not establish a national religion or unduly favor one religion over another.