In almost all cases, Effects and Buffs can adjusted in the Toys MCM.
Reason they cannot be completely disabled, is that Toys is a Framework, and must respect what the mod author "asked for". No Toys MCM option will completely disable a feature that a mod author can choose to use as it could break their quest, either literally, or lore-wise.
There's a plan to, in the future, make it possible for the users to customize toys via the MCM (add/remove their own buffs and effects). In this case the mod author would have the option to turn off customizing for their toy, so now a quest toy would still be in their control, and deny disabling.