Phase Out mechanic is not working
I have found that King of Oathbreaker's ability is not working when he himself is being targeted, where as, per the cards function, he should be phasing out, and therefore his ability should not affect the board. However, he has had an issue where enchantments, a spell, have been able to target him. This should not be occurring just based on how spells are cast and set as designated targets.
When a player says that they will cast a spell on a creature, regardless of if it is from myself or from my opponent, if the card says TARGET creature, not all, then the passive from my creature should go on the stack at instant speed, not sorcery, which means it should resolve first before the initial spell. Annie Joins Up is an example of a cast card that designates to any target creature, but in this instance, and you can try this yourself, it doesn't care about the Oathbreaker passive, and it will just kill you.
Spirits have a hard enough time as it is against other tribals, let alone competitive play. Please fix this interaction soon.

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Kythyll#07463 commented
The damage trigger from Annie Joins Up is considered to be a triggered ability, not a spell, sadly. King of the oathbreakers is protected only from instants, sorceries and auras, since they target as they are put on the stack.