I planted a cacao tree maybe 5 months ago. It's location is between rubber trees with a rather open canopy. I mulched it from the beginning. It has produced a lot of new growth there and since a month or so almost all leaves of the rubber trees have fallen (dry season, much sunshine, 165m asl, thailand). So the tree is a big part of the day exposed to the sun. The tree shows no signs of stress...
The cacao tree is quite delicate. It needs protection from direct sun and wind, requiring a canopy of shade to thrive.
Cacao seedlings often are planted in the shelter of taller mother trees such as banana, plantain, coconut and rubber which provide the necessary shade while also producing other important crops.
Once the cacao trees are established, they can tolerate much more sunlight, but they grow best on small plots of land in partial shade, tended regularly. As a general rule, cacao trees get their start in a nursery bed where seeds from high yielding trees are planted in fiber baskets or plastic bags.
The seedlings grow so fast that in a few months they are ready for transplanting.
We have a bunch of cacao trees on our land. Without sunlight during most of the day they don't grow mature fruit. Their trunks turn a somewhat whitish color by themselves which seems to protect from the intensity of the sunlight here (at 1200 meter above sea level close to the equator). They're slow growing, it takes 3 to 4 years for them to grow to about 1.5 or 2 meters high, some plants take even longer) which is when they start flowering.
I have no idea if the cacao trees described in "old world forestry" are somehow differently from ours... When we planted our first cacao trees we also picked shaded spots because we heard the same thing over and over again, that they are shade loving trees. See picture below. We ended up opening the canopy after our neighbors told us that they won't bear fruit unless they get full sun. They were right...
The Cacao tree is a lot like our Pawpaw tree here in Southern USA, the young tree (germination to year three) is prone to sunburn of the leaves and bark.
This is because both are considered UNDERSTORY trees, they need shade to get going well, then once established they need more sun.
The consensus of the growers I have talked with over the years is that it's best to start these trees under large leaved trees like banana trees then move them once they are starting year three to a sunnier space.
Perhaps what they really need is a shorter overstory so they don't get starved for light just when they are able to handle the extra radiation.
In my neck of the woods I would have to have a conservatory to be able to keep a Cacao tree alive since I am too far north of the equator for them to survive in the wild.
I have only heard of one species of Cacao, but that doesn't mean there are not any cultivars that have been developed somewhere.