Dispenser/Dropper Bug When Item Slots Full
In the 1.1 changelog they fixed hoppers not pulling items from above if all of its slots were occupied. This seems to have broken something with dispensers. Now, a dispenser will not dispense into another one if the receiving dispenser has all of its slots occupied. To test, place two dispensers/droppers facing each other. Fill every slot of one with a single stackable item. Then place one of that same stackable item into the other dispenser/dropper. When you try to dispense an item into the slot-full one, nothing happens.
Linked Issues
Created Issue:
Dispenser/Dropper Bug When Item Slots Full
In the 1.1 changelog they fixed hoppers not pulling items from above if all of its slots were occupied. This seems to have broken something with dispensers. Now, a dispenser will not dispense into another one if the receiving dispenser has all of its slots occupied. To test, place two dispensers/droppers facing each other. Fill every slot of one with a single stackable item. Then place one of that same stackable item into the other dispenser/dropper. When you try to dispense an item into the slot-full one, nothing happens.
relates to
The dispenser will not stack items in another container too.
is duplicated by
Seems to be the same issue as MCPE-22158, will mark as related.
No it's not working as intended but it has already been reported as MCPE-22158.

Confirmed - the dropper will not stack items in another container (eg chest, dropper, dispenser.)
This also affects hoppers, according to
MCPE-23491.Fixed in the latest 1.2 beta.
Fixed in beta build 5