While I don't mix new world, and old world cichlids together in the same "display tank", it is for my own aesthetic reasons, in that I think it looks wrong, and totally un-natural. I might however, in a behind the scenes tank if the combo worked.
I also don't (in display tanks ) use barbs or loaches (most are Asian) with new world or African cichlids, for the same reasons, to me it always looks off.
This does not mean the fish know or care.
I have seen some fish keepers use Mbuna with similarly aggressive North American cichlids like M beani as dithers because of their speed, and ability to withstand the beani attitude when no other fish they tried could.
But I also believe it looks wrong (for me), in a serious display tank, to mix S American cichlids from east of the Andes with those from west.
In S America, you will never find pike cichlids (east of Andes naturally with festae (west), or northern Geophagines, (Sataoperca)with southern Geophagines (Gymnogeopaghus). Beside not being geographically correct visually, the cooler water and winter cool down needed by the Gymnos being the obvious reason.
Or cichlids from Central America, with South Americans cichlids, differences in water type, and higher aggressiveness of the Central and North Americans not with standing.
So in essence, some work, some don't ,(Africa is a giant continent with soft water, hard water, geo type, sardine type, all types of cichlids), and the fish don't know or care (most of the time) its mostly a personal view.Just like hybrids and line bred,I don't want them even if they are free.
I recently saw a post here on MFK, where frontosa were kept with angels, for me not an aesthetic geographically correct option, but quite impressive none the less. And the similar slow moving cichlid attitude between the species seemed to work beautifully, producing a very serene tank.
