None of the headlines that you cite are specific to “extremist Christian-right propaganda”, indeed these are themes are commonly discussed by those who identify as leftist and unreligious, but feel that certain things that are presently insisted on in leftism as de rigeur, are not part of the leftist tradition they recognize from a few decades back. For example, with regard to being “anti-trans”, there are a lot of soixante-huitards who find the current focus on trans activism on the left excessive and even problematic, because it was utterly foreign to their struggle against rightist forces.
You have still not brought forth any proof of your claim above that UnHerd was founded and funded expressly for “extremist Christian-right propaganda” purposes. The gentlemanly thing to do would be to back up that claim, or retract it.