There's a ton of interesting elements to this, but a couple big ones.
1) Conservatives are better than liberals at a version of ideological turing tests. This isn't that surprising where it is understood that conservatives use a wider variety of moral dimensions (things like disgust and in-group loyalty for instance) that liberals tend to use much less, if at all. It is however surprising where they then disagree with liberals on some issues. I suspect this has to do with the stronger in-group loyalties of BOTH groups.
2) The relationship between secular versions of religion to religion. Things like patriotism and nationalism are very, very much like religious institutions, and our political institutions also take on their forms. There's just a different item in the "god" slot. This is probably why I find more common agreement with this sort of assault on religious institutions than on simply disapproving of the whole god aspect to them. Which is by itself a pretty painless delusion. This I also might explain why I find nationalism in particular and patriotism at some level to be offensive and damaging in the same ways that religion can be abused against "others", and why I find something like the Reagan worship of conservatives and especially the rewriting of the Reagan myth to suit new political goals to be disturbing.