Perhaps I'm mistaking Sophronius' meaning, but I took the suggestion about prohibiting government officials from referencing religion to refer more to official speeches/functions. And if that's the point, I actually rather agree with that.
I don't think it's wrong for a government official to admit to being Christian, Muslim, what have you. However, when making an official speech to the country, I feel like the obligatory "and God bless America" is completely unnecessary in the United States. I'm not exactly worked up into a frenzy about it, but I do find it somewhat inappropriate.
Now, I'm not sure if that would be considered a violation of free speech. If my employer requires me to give a speech to my company but tells me to leave all elements of religion out of it, is that a violation of free speech?