Does Freedom of Religion Require the Separation of Church and State?

We assume that the only way to have religious freedom is to separate church and state, but we've had very mixed results. See a recent example here in St. Louis.

Peter Leithart, in his Defending Constantine, argues that Constantine achieved true religious freedom for pagans and Christians. He did this while cooperating with the Christian church to produce a Roman republic with ethical standards and moral development.

Constantine outlawed an ancient version of "no fault divorce," which led to the abandonment of women, gladiatorial games, which littered arenas with bodies, and the exposure of children, which usually resulted in infanticide. He also passed laws that would provide welfare for poor people who couldn't afford to raise a new baby. He reformed the justice system by eliminating they buying and selling of judgeships, and allowed those who couldn't afford an attorney to appeal to an ecclesiastical court.

It appears that the true pax Romana did not occur under Caesar Augustus but under Constantine, and that we often look positively barbaric next to the first Christian Emperor.