What you described as ideal is what the US is supposed to be, and what you described evangelicals as doing is what evangelicals are actually doing, and doesn't really rise above the level of annoying. Maybe they are mentally ill, but that doesn't make them anything beyond annoying.
But people do have a first amendment right to preach. They don't have a claim to a captive audience, though.
He would be so assassinated, so quickly. The IRS does not fuck around. Neither does the Department of Education.