"Not natural allies" does not mean "necessarily enemies". In the "lesser of two evils" sense, I would definitely choose left-wing capitalism over right-wing, just as I would choose liberal Christianity over fundamentalist. But I'm an atheist, not a liberal Christian, and there are elements of liberal Christianity inherently inimical to atheism. In just the same sense there are elements of left-wing capitalism — the capitalism — that are inherently inimical to communism.
In a global society dominated by right-wing capitalism, there are narrow, specific issues where the thinking and politics of communists agrees with left-wing capitalists: e.g. our opposition to sexism and racism and the erosion of bourgeois rights.
But there's a real difference too. While communist and left-wing capitalist intellectuals agree that sexism is bad, we differ sharply on what to do about it. The left-wing capitalist wants to make sure that access to the bourgeoisie is not arbitrarily restricted by sex. The communist wants to eliminate all exploitation of the proletariat by the bourgeoisie, even exploitation that is not sexist.
When it comes to identifying, denouncing and raising awareness of a lot of issues, communists are on the same side as left-wing capitalist intellectuals. When it comes to the solution, however, there are sharp, irreconcilable differences between communists and left-wing capitalists. Left-wing intellectuals want to change the political superstructure only in such a way that it does not affect the basic economic foundations of our society. Communist intellectuals want to change the political superstructure radically enough that it can change the economic foundations of our society, or more precisely to eliminate the underlying contradictions of capitalism that are becoming a fetter on economic productivity.
To do so, we have to eliminate exploitation, not merely establish that the "right" to exploit others is free of arbitrary discrimination.