"Cannot be interrupted" means ninja is immune to skill/chase effect that has pure interruption effect (hashirama senju's chase, iruka mystery, minato mystery, etc.). It DOESN'T provide immunity to debuff with it like immobilisation, sleep, chaos or acupuncture that also interrupt.

To be immune to both normal interruption and interruption based on debuff, ninja has to be immune to debuffs (gakido mystery's effect, root-like buffs or natural one) and immune to interruption (bee 7sst mystery or natural, like nagato, tendo, mifine etc.). This way no matter what hits you, your mystery will go off.

The only 2 mystery exceptions to the above are masked man and shisui's mystery, since they disperse buffs and then apply crowd control, and theres no ninja in the game naturally immune and unable to interrupt. Kushina hanabero c*so interrupt but via chase, because she takes away debuff immunity, so even if that ninja is naturally immune to interruption and has debuff immunity (eg. root), that debuff immunity is taken away and it just leaves you with immunity to interruption, which is vulnerable to debuffs at this point.