To have prayer in public, tax-payer funded schools is to endorse religion. This extends to anyone employed the school leading a formal prayer within a classroom context. A government body, and thus its branches and services, is not in the business of placing one form of thought or reasoning above another, beyond that which can be proven/not proven by scientific and academic means.
Even if a moment of prayer was all-inclusive, donating prayer rugs from Muslim students and other props, it is still placing a moment of importance on theistic belief, and in doing so placing it above non-theistic thought. This is not a war of personal comfort on either side, but of principle. Even if no one is hurt or offended by an action, we aspire to a federal system of placing all ideologies and backgrounds on even footing.