I would not know that a Virginia art teacher has been suspended from his job, due to his students' finding a three year old video of him demonstrating how to paint flowers and butterflies with one's bare rear end. "Although the ACLU of Virginia does not officially represent Mr. Murmer, we are concerned about the constitutional issues involved in this controversy," because "the ACLU believes the First Amendment should protect his right to engage in expressive activities on his own time." The ACLU is right that as a common sense matter, "[i]If Mr. Murmer had not been suspended, the resurfacing of this old video would have probably just created a two or three day buzz before dying out altogether."
However, I do think that government employees can be fired for off-the-job First Amendment activity if such activity genuinely impedes their work. Practically speaking, art teachers usually are known to be weird, so one who paints with his buttocks isn't going to lose much respect anyway. Art classes are supposed to be creative environments, and as long as Murmer makes clear that his particular technique should be practiced only in the privacy of one's own home and never at school, students' giggling about how he looks in a burnt umber thong isn't going to make much of a difference.
I would be more worried if the assistant coach who doubles as the sex-ed teacher (a common duality immortalized in Mean Girls) showed up in pornography. Porn also is First Amendment protected, yet is an expression that would send the wrong message to students who are getting even the standard talk about how sex ought to occur with mutual respect and caring, much less the Bush Administration curriculum about abstinence until marriage. Surely if limiting students' in-school speech in order to maintain a proper learning environment is constitutional, limiting teachers' expressive behavior would be as well. Speech that clearly is speech, and particularly falling within the core aspects of the First Amendment -- say, a biology teacher required to include evolution on the syllabus who publicly supports intelligent design instead -- is making a political, scientific, religious statement that should not be grounds for dismissal even if it may conflict with his educational role. Yet behavior that runs contrary to the ideas and values the school attempts to inculcate, such as a writing teacher who becomes known for plagiarizing, even if it includes a First Amendment-protected element, should be subject to policing.