I would not describe the defining parts of buddhism as ideological so much as philosophical and sensuous. I’m not sure a good definition of religion exists. You’re being hugey reductive.
In the non-jargon common sense of ideology ("a system of ideas and ideals, especially one that forms the basis of economic or political theory and policy", thanks dictionary) you're broadly right.
If you remove all the cosmology and mysticism from Buddhism, you are left with something other than the original practice.
Like a dictionary? It's just semantics