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 this context, Zizekian "ideology" is a set of beliefs or axioms that color how we perceive the world. It's just the medium through which we live our lives and exist our existences and engage with social structures. So in that sense, religion is one thing which would help to make up 'ideology'.
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.
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.