A couple of questions.
Have you discussed this with your priest?
Likewise, I am surprised that a public high school is allowing religious groups in the first place. do you know why these kids asked you as apposed to another staff member? Do you know what Mosque most of the the students attend and what that mosque is teaching?
You are not obligated to show that you are “fair and open minded”. Sometimes, we can be so open minded that our brains fall out. Islam is a very aggressive proselytizing faith and student groups like this are meant to spread Islam among unsuspecting students. I guess i keep thinking of an eight year old Catholic boy, standing watching a parade when some nice (everyone who knew him said that) Muslim boy that went to an exclusive high school, wrestled, was on school committees, went to the prom, was awarded 25K to go to school plants a home made bomb at his feet. It kills him and maims his mother and sister for life.
Yet, we get so worried about being seen as fair and open minded towards Islam that we are willing to forget an 8 year old Catholic boy that is now dead that was killed in its name who will never now go to the prom, wrestle, or have the chance at any scholarship. In honor of that lost child, I would politely turn them down.