“Christianity is itself an ideology.”
I believe it is not. (Perhaps there is a ‘faith’ pun there.)
All other religions are. (Human nature desires structure, rules, etc. for security. But humans cannot follow the rules (any rules). Islam as we see it appears attractive today for these reasons.)
Ideologies do not work. That’s why Christianity is different, and why God is the True God.
You are defining not the difference between ideology and not-ideology, but rather the difference between (what you believe) to be True ideology and a variety of other ideologies that contain elements of truth and error to varying degrees.
That a belief system is True does not make it any less an ideology.