People's political views are generally interwoven with their notion of morality and in the case of the religious, that morality is informed by their religion. The idea that you can separate religion and politics is misguided at best.
Also, even if you remove religion something else will surely take its place. It seems that notions of aggressive conventionality and "crush the unclean" are somewhat baked into a percentage of society, and I definitely think the really hostile climate of the pandemic has added evidence to this theory. There's always going to be a nasty, moralistic, curtain-twitcher segment of society no matter what name or organisation they give it. Sometimes they hide behind religion, sometimes they hide behind politics, sometimes it's another label entirely but what they all have in common is an excessive bias when it comes to the emotion of disgust.
I'm certainly not anti-religious (I'm no atheist myself), but I'm very anti-moral crusading against the business of consenting adults whatever form it takes.
The Unholy Trinity: State, Church and the Market. Despite the common belief to the contrary, they can never be truly separated. They're only distinct in the sense a continuous multimodal distribution has "distinct" modes - the boundaries are fuzzy. Ultimately, they all serve the goal of social coordination, and they all work with means of coercing people to do things for other people.