Most of the universities I can see on that list are not religiously affiliated.
I think that in our quick-pace life where old technologies are 20 years old, we sometimes forget that the world is an old place.
In the case of the older educational institutions (e.g. King’s school, Bologna), the dividing lines between church and state were messy and overlapping and even now if they are not religiously affiliated their roots may lie there. My high school is “merely” 350+ years old (predates Newton) and started out with a curriculum that was mostly bible and classics although it would be considered unaffiliated today.
I used the two words longevity and continuity because something can be old but have transformed unrecognizably, or close thereto (e.g. while amcountry may be ancient, the monarchies at its head can change radically. Likewise even some ancient commercial enterprises).
It's not that corporations can't exist for that long. It's that they're much less likely to, and are thus a poorer bet for the survival of an extremely long-term project.