Some might argue the opposite, that said I agree that the way many people approach religion makes it basically equal to an ideology.
But you can approach religions as a topic in countless ways, so I think it is fair not to reduce it to the lowest (albeit maybe most common...) approach people have
Religion has elements of ideology, some ideologies are derived from, related to, or specifically opposed to religious belief. That last might be an XOR.
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.
But you can approach religions as a topic in countless ways, so I think it is fair not to reduce it to the lowest (albeit maybe most common...) approach people have