It should be abundantly clear that the Constitution’s “no religious test for public office” clause is a crucial piece of the separation of church and state. Contrary to Ben Carson, who would oppose a Muslim from holding office; contrary to Bernie Sanders, who discounted a Christian appointee who, privately, affirmed that Islam possess a deficient theology; contrary to Diane Feinstein, who fears Christian dogma, the state possesses no authority or competence to render judgment on the confessions or confessors of any house of worship.
Has our nation been benefitted or harmed by the No Religious Test clause of the Constitution? That depends on who you ask and to what extent. An open society that accommodates multiple faith traditions ideally works better at promoting genuine faith than one that indoctrinates its citizens and threatens dissenters with violence. The latter creates hypocrites, while the former facilitates the unhampered pursuit of truth.
The framers anticipated Bernie. The “Machiavellian Golden Rule” codified in the Constitution has for two centuries withstood the attempts of factions to benefit from it themselves while violating it for others. The founders discovered a workable way of peacefully arranging this society of religious and anti-religious zealots such that, while no sect gets everything that it wants (to dominate), neither does it get what it doesn’t want (to be suppressed).