Whether they are irreligious or religious, their position is that of governmental minimalism. Christian nations such as the United States pre-1933 can follow governmental minimalism. Other nations styling themselves as Christian, such as Calvin's Geneva, England under Elizabeth I and Cromwell, Spain during the Inquisition, etc., were tyrannies with secret police, star chamber proceedings, and suppression of religious dissidents, including theft of their land, slavery, and mass murder.
If you want to talk about policy matters, most people who are styled conservatives today oppose abolishing the welfare state, restoring the gold standard, and eliminating Federal police agencies. As stated earlier, most modern conservatives are closer to New Deal/Great Society policies than to those of Harding and Coolidge. At most, they oppose further expansion of the welfare state, e.g. Obamacare.