I don’t think Mo Xanyu would be into incest? (however it is up to the authour) Since Yao is his half brother,,, ALSO SPOILER FROM THE NOVEL BELOW!!
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If I remember correctly, it’s found out that Yao did kick out Xanyu and branded him a cut sleeve/maniac because Xanyu had seen something he wasn’t suppose to see.
Argh lol that novel was so long that I cant remember. MXY was definitely a cut sleeve as far as JGY making the harassment up I dont remember :/ I seem to remember it being legit and the incest thing made it even more scandalous but JGY is rly clever so maybe he made it up to get rid of a possible contender for clan leader. Remember he went on a purge to get rid of all his half sisters and brothers who could potentially compete with him so maybe instead of killing MXY he just banished him. <that's sound plausible
But we only get info on MXY at the beginning of the novel and trough other characters about who MXY was. It was never confirmed what was truly done, it's literally up the person reading. Not sure if drama added something more, but i don't take it as canon.
The reason I think MXY harassed JGY is for the simple reason that JGY was probably kind to him in a sect full of hornets. Facade or not, JGY somehow let him get close enough to that secret room of his (or was this NHS who sniffed it out? can't remember this bit). I'm willing to bet JGS never showed MXY any love/recognition unless he was threatening JGY. Plus we have the makeup thing going on and JGY doesn't go after someone unless they attacked him first or it was an order from his father.
All in all, MXY is completely a mystery

still wonder if mxy actually harassed jgy or if jgy made that up to kick him out of the jin sect