Magic uses very precise terms. An ability getting activated, and thus being prevented from being activated, is only possible for activated abilities. Sheoldred doesn't have any. She has triggered abilities. Triggered abilities don't activate, they trigger. And Planar Disruption doesn't prevent triggered abilities from triggering.

And Magic defines those two kinds of abilities as follows:

An activated ability is always written in the form [cost]:[effect]. There is always a cost, followed by a colon, followed by the effect(s) of the ability. For keyword abilities, this template is found in the rules for them. Activated abilities are chosen by players to be activated.

Triggered abilities always start with the words "when", "whenever", or "at", and the phrase using that word states the trigger condition. Triggered abilities trigger whenever their trigger condition is met, no players have any say in this.

Arena is treating this card like pacifism and it’s not