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> I recently saw fascism described as a version of collectivism that caters to the right.

Yes, I think that's its definition.

> Perhaps conservatism doesn't necessarily fit into a left-right spectrum neatly.

While conservatism is right, right isn't necessarily conservatism. Conservatism more describes a center-right party, the extreme right often is what is called fascism, with one alternative being fundamentalism. I think conservatism and fascism are pretty much mutual exclusive.