The First Amendment has two parts.  The first, which you refer to, permits people to practice their religion.  The second is the establishment clause - by continuing with the invocation but only allowing religions they approve of, they are skirting the boundaries of that.

Unless they're willing to have the invocation given by practitioners of other religions they are in the wrong and the first time they refuse an Islamic invocation I fully expect to see them spending some serious taxpayer dollars defending themselves.