Basically, they're apeshit tribalistic of their turfs:
Situationists rail against all forms of SPECTACLE and conformity, including the Fascist kind.
Rexism formed as a reaction against the degeneration of traditional values, directing most of its ire against radical Geoists in Spain and Russia.
Socialist resembles its OTL namesake the most.
Geoists though are incredibly jealous of anything urban, further making the Socialists irrelevant in politics.
All of those ideologies formed due to the civic and nativist nationalism that Fascism made especially in constructing a framework for an "end of history" in the 30's.
Societists though? They've sided with the degenerate Geoists and espouse heretical and Un-christian values. Those, especially the former, are the things that made even the most virulent of Rexists hate the ideology.
@Born in the USSA 's description is somewhat apt here; only that instead of OTL Fascism railing against both capitalism and communism, here it was directed purely against TTL Fascism.
So no, there's five distinct and mutually irreconcilable ideologies here as of late: Rexism, Societism, Situationism, Fascism, and Geoism, each having their
own goals that had been ideologically exclusive of each other. For Rexism, the supremacy of Tradition; for Societism, the supremacy of the custodian race; Situationism, fun; Fascism, democracy and nation; and for the Geoists, effective land use and resource exploitation.