Looking at the species of self-confessed modern conservative in the Anglophone world, it’s quite likely they are mostly also self-confessed people of religious faith.
One of the most pronounced and intractable political biases in Australia’s election environment comes from a core of notionally educated, engaged people who regard it as a heresy to agree with anything connected to the the labels ‘Coalition’, ‘conservatism’, and ‘right’. Not that this might be unjustified, except that the bias extends to believing that everything the ‘progressive left’ or ‘Labor’ does is OK, regardless of what that might be.
Such people might be thought of as bien pensants (right-thinking, self-righteous), a French term, originally implying people who repeat orthodox, conservative prejudices, but now also those who adopt and repeat ‘fashionable’ ideas without critical analysis or judgement. Ultimately, and ironically, that latter definition is actually the meaning of unthinking conservatism, even if so many bien pensants today believe themselves to be progressives or left-leaning.