I’m under the impression they are (were?) allies of convenience and didn’t have a lot of love for each other.

This goes for almost all of the loosely affiliated right-wing organizations currently under the umbrella of the administration. It’s our best bet for the future; drive a wedge between them, make them fight each other rather than us. Use their own tactics against them. Cfr the Trump-Musk feud. There’ll be others. There’s also the succession war in Murdoch’s circle. He’s still fighting against his sons (who may legitimately be even more batshit than he is). It must be so frustrating for someone like him to ‘build an empire’ and see it being divided before their death.