If A's religion says "there are these gods, and they like us to do X", and B's religion says "there are those gods, and they like us to do Y", then there's a reasonable chance that you can combine them to say "there are these gods and those gods, and they all like us to do Z, and some of them also like X-Z and some like Y-Z".

But if A's religion says "there are these gods, and they like us to do X, and there are no others, and the will of the gods is a universal truth that applies to everyone" and B's religion says something similar, then unless one can credibly argue that these gods and those gods are the exact same gods and that X and Y are the same, there's not much prospect for syncretism.

The world's two largest religions, Christianity and Islam, are both very much of the latter type. There is One God, and he is The Only God, and his will is Absolute Moral Truth, and any other so-called god is necessarily a false god, meaning (in the most optimistic case) something people just made up in error, or (in the not so optimistic case) a supernatural being who ought to be subordinate to the One True God but is in rebellion against him and trying to sow confusion and error and evil.

If you have a religion of the second type, any sort of syncretism involving that religion pretty much has to have (at least) some sort of insincerity or sloppiness or something about it.

Political ideologies aren't necessarily more like the second sort of religion than the first, but often they are, especially when considering them in relation to other political ideologies competing for the same people. If A's ideology says that the most important thing is the distribution of wealth, and that rich people mostly get rich by taking wealth that ought to belong to poorer people, and the rich are holding the poor down for their own (the rich's) benefit, and B's ideology says that the most important thing is the distribution of wealth, and that rich people mostly get rich by providing the world with valuable things and capturing a small fraction of the value they create, and no one is holding the poor down but themselves, and if A and B are operating within a political system where one can gain only when the other loses, the prospects for a syncretic combination of the two are remote.

But ... actual real-world political parties are themselves kinda-sorta syncretic entities, at least some of the time. There isn't any very compelling reason why economic libertarianism and social conservatism and preference for Christianity over other religions or absences thereof and dislike of immigration should all go together, but there they all are in the Republican Party (and in its rough equivalents in some other countries besides the US), and you could say similar things about the coalitions that constitute other political parties. Unfortunately, when you have two equal but opposite syncretic piles of ideology, the fact that each of them is full of syncretism doesn't do anything to make them more willing to cooperate nicely with one another.