At the end of the day, the species that are going to be best suited for living with a particular species are the species that already do exist with it in nature.
It's not so much a matter of being strict, as it is being realistic with what is best for a stable fish-tank in the long run.
There are many fishes that care far less in regards to water, or tank-mates- but in the same vein there are many that do.
As Duane said, the water-chemistry matters a lot with many species, and not following it can lead to complications down the line.
Like altums, and wild discus, that are adamant about soft water with almost no TDS or conductivity. They are no less a cichlid than a Haplochromine from Lake Malawi.
On top of that, a fish-tank is highly unnatural, and brings out odd behaviours in fish; viewing how they act in situ makes it all the more clear.
For instance, a lot of Crenicichla (especially larger spp.; saxatilis-group/Saxatilia, lugubris-group/Lugubria) are seemingly rather passive in the wild, and oftentimes form large shoals.
In captivity, they are regarded as fiercely aggressive and highly territorial to the point of being intolerant of other tank-mates, because the given space they are forced to inhabit is substantially limited.
I think the question is too broad to be able to answer it well- after all, there are answers that apply to all fish, such as any fish that is excessively territorial/aggressive, a fish big enough to eat the cichlid, a fish that will be harassed to death or killed/eaten, etc.
You did elaborate on wanting to know of fish that would be able to eat a large cichlid... but to me that would be almost any larger predatory fish; and you did sort of answer your own question by pointing out the obvious mainstream examples- there aren't too many others that are going to be found that an aquarist would keep with an aggressive Parachromis/Andinoacara/Cichla because they would know better than to do that, if they seek out such species (like many of the predatory Asian cyprinids, Lake Tanganyikan Lates spp, larger Silurus spp., etc)
I myself prefer to keep cichlids either in a species-only setup, or as a 'biotope'-type setup with other species from similar/same waters.
Then again I mostly do this because I prefer keeping smaller Geophagini and 'dwarf' West Africans, that are more sensitive and particular about their water and tank-mates.
. I think large cichlids can overcome piranhas, but their instinct is to fight by lips locking, yep, doing that against a piranha is already a lost, but I've heard of some people managed to cohabit piranhas with oscars(somehow). Maybe the amounts of fish in your tank wasn't a lot? Anyways, how do people get RTC to live with oscars and large cichlids without RTC eating all of them long term? Is that even possible? Is there any trick? Just curious. Anyways, I'd trust a tiger shovelnose more than a RTC, hahaha.
