after reaching reaching the level that requires you to pet 20 different mobs to progress; the player loses the ability to interact with any pets/animals in the standard manner. this means players can no longer mount horses (or other moutn based mobs from other mods such as dragons from ice and fire, or any mount based mob from Lycanites mobs, the horses from vanilla or the horses from Animania, And all basic pet interactions such as picking up and placing your pet hamsters on your shoulder (also from Animania) just to name the bigger conflicts this ability causes.

I have a simple solution for this issue. - Edit the event trigger of the action so it functions only when the player presses right click while holding the sneak key, instead of when the player simply right clicks at all. This way the effect of petting mobs can still be performed without conflicting with basic minecraft functions and the functions of other mods in the process.

do these interactions work when holding things other than proper tools or perhaps with tools or do they specifically require the use of empty hands? Since you can mount horses with any old rightclick and same with sitting/unsitting stuff, but the hamsters I'm not so aware of.

empty hand interactions and as the "pet animal to heal and make it happy" from the monk powers needs an open/empty hand to function to begin with currently, and that's how i noticed these right click based functions weren't functioning as intended with the monk mod installed after receiving the ability at level 4 within the monk mod's level of skills/abilities

BUT! dragons from Ice and fire mod can be mounted with an empty hand or with an item in hand so long as you right click them, and these functions no longer functioned while the "ability" in question was over-writing all registered right click functions, preventing the player from doing anything aside from "petting" their pet dragon. - reguardless of the tier trying to be ridden (thought to be clear; it was a stage 5, which is full grown and normally in the ice and fire, the player has to have their tamed dragon at a minimal of stage 3 (or higher) to mount them in the same manner as riding a horse.

 All mounting based features from vanilla minecraft and other mods that provided unique mountable creatures (ice and fire, Lycanites mods, Animania just to name a few)
   As well as the few the cases where the player could normally pick up their pets (such as vannilla parrots, hamster from Animania, and tamed dragon of stages 1 and 2 from the ice and fire mod) could no longer be interacted with via right clicking them with or without an item in hand so long as the player had the ability to "pet animals to heal them and make them happy"

the issue above ceased being an issue when the Monk mod was uninstalled and all other existing mods remained. Further more this issue had only begun when the ability itself was unlocked within the leveling system provided by the Monk mod. and the issue persisted again when said ability was unlocked once more after re-introducing the monk mod in a newly generated world that used all the same existing mods prior. -just to double check that this was the exact point of origin for the bug/conflict in question.

I hope that these furthered details explains the nature of the issue itself better, and that a solution can be found to correct the issue in question with the ability. -- if the ability itself can not be corrected to remain as a passive ability without constantly causing these conflicts, then i would again, recommend coding a manual key binding for the skill itself the player may choose when to toggle on the ability and when to toggle it off, as to prevent such conflicts from actively ruining basic minecraft mechanics and other mods in the process.

as i originally posted on the Monk mod's comment section; this mod has potential to be one of the best mods out there that introduces new gameplay to minecraft. And i still believe in that statement i made, that's why i'm addressing this issue here so passionately.