Werebeings in D&D are powerful characters who are capable of transforming into specific beings, notably tigers, bears, and wolves, or hybrid human/beasts. The rules concerning the question are as follows (these rules are for weretigers specifically, but they apply across all werebeings):
The weretiger can use its action to Polymorph into a tiger-humanoid hybrid or into a tiger, or back into its true form, which is humanoid. Its Statistics, other than its size, are the same in each form. Any Equipment it is wearing or carrying isn't transformed. It reverts to its true form if it dies.
The as-written rules seem to indicate it is a form of the polymorph spell, which states that
The creature is limited in the actions it can perform by the nature of its new form, and it can't speak, cast Spells, or take any other action that requires hands or Speech. Boldface added.
As such, it would seem that a transformed character couldn't cast spells, but what about the hybrid?
The hybrid is fairly ill-defined, and when designing a were-creature (particularly a spellcaster), it would be paramount to know, can a werebeing in hybrid form cast spells?
Best Answer
Yes
The ability is not the Polymorph spell
The weretiger cannot possibly be casting polymorph, because polymorph requires that the target change into a beast. However, the hybrid form is distinctly a humanoid form. We can deduce this because the ability says:
Monster statistics include type. Which means that even in tiger form, the weretiger is a Humanoid (Human, shapechanger).
Polymorph says that:
If the weretiger were casting Polymorph, its type would change. But it doesn't, so the creature isn't casting Polymorph. Therefore the rules for the Polymorph spell do not apply.
They can use weapons, which is probably good enough for somatic components.
The actions of the weretiger allow for the hybrid form to use weapons, with no penalty compared to their normal humanoid form. If their hybrid hands can wield weapons effectively, then there is no reason that they can't manipulate material and somatic spell components with similar ease.
Hybrid forms can still speak
The stat block for the weretiger allows the creature to speak in all forms except tiger form. Thus, the hybrid form can provide verbal spell components.
So, we have established that the limitations of the polymorph spell do not apply, the hybrid form can use weapons and so should have the dexterity for somatic and material spell components, and they can still speak to provide verbal components. Thus, in hybrid form, a weretiger can cast spells.
All other werecreature hybrid forms follow similar structure as the weretiger to my knowledge, and so should work identically.