I’m naturally oriented towards systems-thinking and an ideology is a construct of ideas that in totality makes a system. An easy example would be religions that tend to consist of metaphysical ideas, ethics, aesthetic ideas and epistemology.
For instance in the Christian religion
“God exists” is a metaphysical statement.
The ten commandments and the Golden Rule are ethical ideas, based on deontological ethics and objective ethics.
The design of the temple, the stone tables are aesthetic ideas.
Knowledge comes from divine revelation is epistemology.
There is a lot to be learned from deconstructing an ideology in this manner. For instance, you get to the bottom of what axioms are required in order for the ideology to be “true” and whether it is logical. You learn whether it is built like a house of cards or as a pyramid.
Some have taken to calling atheism an ideology, if Atheism is broken down into fundamental ideas there is really only 1 core statement in Atheism, which is the answer to the metaphysical question “Is there a god?”.
Atheism has no statement of ethics or of aesthetics. It does tend to view epistemology in the traditional western logical systems and scientific method. However, this is not a prerequisite. So, in this sense, Atheism isn’t an ideology, it is a conclusion.