OED defines fascism as “an extreme right-wing political system or attitude that is in favour of strong central government, aggressively promoting your own country or race above others, and that does not allow any opposition”

It has this to say about liberalism: “having or relating to political and social beliefs that support individual freedom and rights, democracy and free enterprise (= businesses competing against each other with little government control)”

I do not feel that these are incompatible in any major way. Prolewiki does do a better job of pointing that out, but I still think the OED’s definition works as well.