If you clear the public square of what we traditionally call religion -- Christianity, Judaism, Islam, Mormonism, Buddhism etc. -- we will not have a public square free of religion. We have a public square full of religion fighting under the false flag of "secular values" -- with no opposing sources of moral authority to resist it.
The utopianism, millenarianism and radical egalitarianism at the emotional core of liberalism are fundamentally religious in nature. That doesn't mean liberalism is evil or totalitarian. But it is less than totally self-aware. The nice thing about traditional religion is you know where it comes from. The unwritten faith of liberalism masquerades in the costumes of modernity, progress, social justice and the like without recognizing that liberalism requires leaps of faith, too.
Liberalism's lack of self-knowledge about its nature makes it very powerful and very dangerous. Liberals can simply claim -- without seeming like they're lying, because they actually believe it -- that they are cold, rational presenters of fact and decency. Comte's "religion of humanity" has forgotten that it is a religion at all. But forgetting something doesn't make it any less real. Wile E. Coyote forgets there's no land underneath him. His ignorance doesn't keep him aloft.
This is how the New Class of experts and helping professions become secular priests of a wholly political religion. We confuse credentials for ordinations, regression analyses for consecrations. And without a conception of a higher authority, without a more enduring and transcendent dogma to inform our consciences, we are left following the captains of rudderless ships leading us to ruin.