Does using fates call interrupt/cancel passive abilities and active spells of the Oathsworn?

Kalista's ultimate Fate's call makes her Oathsworn untargetable and invisible as well as not allowing the Oathsworn to cast spells. My question is this if you use fate's call on a target using an ability that has a passive element will that passive element be disabled as well.

To be clear and to offer context I'll use rengar's ultimate as an example. He goes invisible and when he is close to an enemy champion that champion is alerted, this is passive rengar has no control other than not being in range of the target. So I wanted to know, if Kalista were to use her ultimate on rengar would enemy champions near kalista get the notification that rengar is present, if kalista pulls rengar after he goes invisible.

No It does not (at least for the most part). Any effect that is active during Zhonya's will persist for the time the Oathsworn is invulnerable. This includes spells such as Wukong's ultimate and Fiddle ultimate but even effects like Rammus' Powerball will remain Active. This is also one of the reasons why Kennen support is so popluar combined with Kalista (His ult is easy to reposition).

Here is a small video that demonstrates some of the effects:

Note that while this is labelled as "bugs" all the effects in the video I've described above are working as intended on the Live servers

For your specific question about Rengar: His stealth would be cancelled since it's being cancelled by actions, however the other effects that remain during stasis (Auras, Most AOE ultimates) still remain active.