The question here is “Can you mix cichlids from different continents?” The short answer is “yes,” but a better question is “Should you?”
Like many answers to fish keeping questions, the answer is “maybe.” As a general rule, cichlids from different continents live in different water conditions. For example, black water species from Amazon River tributaries (e.g., some Apistogramma, Chrenicichla) thrive in water vastly different from cichlids in Lake Tanganyika. The pH alone in these two bodies of water is very different, not to mention other parameters (TDS, hardness, etc.). Yes, there are multiple exceptions. Some species in Central America (CA) share similar, hard and alkaline water as their cichlid cousins in the African rift lakes.
In addition, not all cichlids share the same diet. Yes, many herbivores, carnivores, and omnivores share the same water. However, it is usually not a good idea to mix species where one primarily consumes plant matter and one primarily consumes animal matter. This does not set you up for long term fish keeping success, unless you can ensure that each species gets the appropriate food.
On the other hand, there are many species from different continents that share nearly identical water parameters and consume the same foods, nutritionally speaking. For example, some CA species and African rift lake species both thrive on a diet of insects, smaller fish, etc.
Another factor to consider is temperament. Not all cichlids are vicious, but many are and thus not all cichlids should be kept together for that reason alone, especially if they don’t co-exist in the wild.
So, to repeat, “Can you mix cichlids from different continents?” Yes, you can. However, you should understand the needs of each species before you decide to keep them together. Know the water, the diet, and the general temperament of the fish you plan to keep. Your best bet for success is to not keep fish together that are incompatible in one or more of these areas. Doing otherwise sets you up for failure. It might seem to work fine in the short term, but the probability of you experiencing problems is quite high when you mix the wrong species.