Yet since Richard Dawkins is very well known, even to the average member of the public, as a virulently anti-religion person, any appearance by him in the public schools could easily be taken as implying a tacit endorsement of the public schools for his religious views. I think there would be a strong constitutional case for banning Dawkins from speaking in public schools, given that context.
If you think that Dawkins should be allowed to teach about evolution in public schools as long as he agrees not to mention religion, that might sound fine in principle, but remember the case of Bertrand Russell and the City College of New York. A judge in a lawsuit involving Dawkins might rule the way the judge ruled in the Russell case.