Partly a product of social media, the way we talk about those with whom we disagree has changed a lot.
In particular, at the risk of sounding partisan, here is the way I see those who view themselves as “progressive” (what a terrible name to give yourself) engaging religious conservatism: Instead of talking to people about why they disagree and why they think people of a conservative bent should change their minds or behaviour, they talk about them to the world. When they do so they are not critically engaging with them (even if they tell us that this is what they are doing). Instead they are serving the social function of shaming them, not so that they will change their mind, but so that they will be afraid of speaking.
Many progressive Christians, if I have observed things correctly, think that they are the real followers of Jesus (who, we are told, was an inclusive, tolerant, liberal-minded progressive), while religious conservatives are more like the religious hypocrites from whom Jesus distanced himself. Sweeping generalisations are usually wrong if taken as hard and fast rules. This description is true of many religious conservatives, no doubt There are plenty of them, after all. But to a large extent it is self-flattering nonsense. While many progressives like to say that religious conservatives “pick and choose” which commands of Jesus they follow, sometimes it’s helpful to hold up a mirror to this outlook, if only because of its irrepressible self-confidence in being real, authentic, pure-as-the-driven-snow, Jesus-following Christianity, along with its current occupation of a position of social power, something Christians are justified in being suspicious of (let’s remember that it’s not just a worrying combination when it’s manifested in the religious right).
Progressive Christianity, had it existed in the first century, would have found opportunities to shame Jesus himself.