There is no formal alliance. However, there is de-facto cooperation, for example, right-leaning anti-criticalist commentators who would give gender criticalism a free pass, or gender critical feminists who would go to events hosted by conservative organizations like the Heritage Foundation, who they are otherwise at odds with.

My main concern is that, this kind of unprincipled cooperation furthers the polarization, which isn't constructive, unlike voices from the center, e.g. Andrew Sullivan who I wrote about last week, who has concerns about trans activism but still aims to be constructive.