Uh.. no?
And each ideology has a specific history of events, founders, and later elaborators that shape what these rituals and beliefs are.
Many ideologies reject deities or are at least ambivalent about them, but they're not really operationally different than religions.
So for as much as little bits of history linger in relgious rituals, both blurred and resharpened in later years, the same is absolutely true for ideologies.
The capitalism or feminism or humanism or atheism or whatever else you point to today is similar to the one sharing its name in the past, or in some other region, but is not the same, and these differences are all vestiges of little seed events that happened here or there.
An adherent of an ideology might, like, have rituals. But the ideology isn't the rituals.
Here are some ideologies off the top of my head: democracy, marxism, environmentalism, libertarianism, atheism, the moral basis of Christianity but not the religion itself, utitarianism, humanism, empiricism.
None of those have, as far as I can tell, a single ritual inherently associated with them.
(You'll also have a hard time enumerating those concepts in a complete and consistent way)
But if you're even a wee bit of a subjectivist, as many (not all) social scientists and social philosphers are, then a definition like that isn't interesting or productive. From that perspective, ideologies are something that people profess adherence to and express statements about and behave in self-identified accordance to.
They gather in elections, they discuss power through the lens of capital and labor, they recycle or avoid eating meat, they recoil at government overreach, they expose fraud in purported miralces, they pray, they trade trolley problem memes unironically, they protest against inequality, etc
If these don't make sense to you as "rituals of ideologies" for people doing cross-cultural studies, that's fine, but then I have a sense that a lot of cross-cultural studies just feels like hogwash to you anyway. I doubt I could change your mind here. :)
(nor would I call any of those rituals, either, but I guess words don't mean what they normally mean in those fields)
If you earnestly wished to "see the point", you're tripping yourself with by taking for granted "what it means to everyone else.." and things like "living in idea space"
There are traditions of study/thought that use ideology the way you mean, and traditions that don't. The variety of use is well-represented and has been since the word came into use. Likewise, "idea space" is a specific concept that some people accept as sensible and others don't. Again, the variety of relationships to it is well-represented (and stretches back millennia, on that one).
You can actually see an example of this kind of differing-perspectives-in-wide-use in the way use used "the moral basis of Christianity but not the religion itself" in your own comment above. While Platonic ideas predate Christianity and have much influence on its shape and study in the West, the that statement would strike most traditional and many modern Christian thinkers as non-sensical. To them, there is no sensible separation of Christianity's "moral basis" from its Church/people and trying to make some distinction is as alien and "pointless" to them as different senses of ideology are to you.
And yet, of course it's interesting to think about Christianity's "moral basis" as an ideology existing in "idea space" because it lets you relate that part of Christianity to other things that you feel are comparable using techniques that you know how to work with and have confidence in. That's pretty much exactly what's going on with social scientists/philosophers who think about ideology in the way I've been describing above.
Some, but not all of those rituals even stand up to basic scrutiny. Others, not so much.
Like, at its core, all it says is that there's one god, and he was his own kid, who died, and there's an afterlife, and you should live well.
Yet, I don't think you'd say that Christianity doesn't have rituals, even if no particular instantiation of it has the same rituals as any other one.
Interestingly, how to (or if we even should!) resolve such issues in our (use of) language is itself a highly ideological matter.
If you simply consider how the human mind works, this "should" be fairly obvious. But one's ability or likelihood to think about such things is once again a function of the norms and accepted practices of one's ideology. That which is not known of, essentially does not exist.