Ideologies can be thought of as archetypes. Imagine the communistic ideology as an archetypal bearded Marx sitting inside the skull of Marxist activists. Every time you speak to someone espousing Marx, they say the same thing, and make the same arguments, because they all carry that same set of beliefs. This is true for Christianity (bearded Jesus), Capitalism (bearded Uncle Sam), Christmas (bearded Santa)…starting to see a pattern here…
Moving over to systems/information theory, every “set” of beliefs in your brain is like a tiny set of instructions about how to process information (e.g. seeing red, green, white lights on tiny bulbs means Christmas, but not Easter). Each separate grouping of beliefs is packed into its own little box, and anytime you encounter information in the world that you think is relevant to the beliefs in that box, you run the information through the box and see what spits out. It is the case that one can process information through many different types of boxes, i.e. seeing a statue of Christ as a devout christian is not the same thing as seeing it as a militant atheist. In fact, part of the ability to process information through many different boxes is called thinking critically.
It is important to understand that we are all in possession of ideologies. There are probably dozens of high-level heuristics about how to see the world running in your head all the time, and countless more unawares. The manner in which you notice the swiftness of the people walking around you, or the number of smiles you get at work, or the amount of skin your coworker is showing today; all this gets processed via some heuristic which is often neatly expressed in language by a social ideology (prude, modesty, politeness, hurried). The key idea that Peterson attempts to teach is that, though you are in possession of many ideologies, you should try as hard as you damned well can not to be possessed by them, and especially not just one of them, and even more especially not a bad and impoverished ideology, like Intersectionality for instance.
When you choose to filter everything through a single ideology you are ignoring an extraordinarily large swath of reality, and eventually it will come back in the form of a dragon and bite you- and interestingly enough, since you were the originator of that poorly filtered ideology, the dragon is really biting its own tail- you are the tail. It is this realization that Peterson wishes to teach, that the creature that hounds you, the ills of your culture, the sufferings at home, is ultimately traced back to this improper filtration of reality through too narrow and too incapable an ideology. The blame for all our ills lies on the great transpersonal failure of our collective living group to meet the challenges of reality. But, if we pay attention, and use language to communicate to each other our own failures and successes, we can continually improve our heuristics. This process of continual improvement is the real identity of the conscious self. You are not a robot to spit out other people’s programs. You are the programmer sitting atop the robot that God, and the billion ancestors before you, gifted you.
TLDR; Yes, Peterson has ideologies, we all do. And yes, you can analyze each and every one of them for their usefulness or truthfulness. That’s exactly what he’d hope you do.