
It all makes pefect sense :)
All the "friendship" was fake. All the time he was only ass-licker and we saw it. He just wanted to establish his power and influence (as well as his whole family). That's why he was frantic about Nok dying in the forest.
However when he found out Nok's gay it automatically meant he won't ever gain what he wanted from him. And was fuelled by strong homophobia and probably hatred for Jaeshin.
So he went for the last possible way - the queen (or more precisely - her son). Choi Kyeong Jun thinks she wants to kill Nok just for the position of the crown prince, to put her son in these shoes. When Nok would be deposed there won't be any reason to kill him (in Choi's mind).
P.S. Now when I'm thinking about it, if Choi will find out about the queen's deeds and evil spirit he might change again. Or just go crazy bc he's prim and proper (with a stick in his ass;))

The thing is Choi knows the queen is the source of all the evil sorcery going on and he knows she's the reason why people keep dying around Nok lol
They have a discussion about it early on in the series and it's hinted that Choi knows this when Nok rejects marrying his baby sister for her safety. He also knows that dabbling in something as evil as sorcery is one of the worst crimes you can commit when you're a part of the royal family. They literally killed the previous queen for it even tho she did it to protect Nok from Chae-hee.
I get that he's a self-fulfilling asshole, but I feel like someone being gay or having gay relations is a lot easier to hide or rationalize than someone literally casting curses on multiple (('cause Chae-hee is also cursing her son to keep him sickly)) royal family members lol even tho it was frowned upon, it wasn't uncommon for nobles to dabble in sodomy so long as they didn't marry another man. Male kisaengs are a thing for a reason.
That's why I said his gat is too tight. Like, it he gets busted siding with the queen he's fucking dead lol he'll be executed along with her and anyone who worked with her. He's potentially putting his family at risk siding with the evil witch queen lol

Like you've said, it's not uncommon to assassinate here and there. Choi probably knows nothing about poisoning Daegun. He doesn't know she's possessed and actually, with her own hands, leads ppl to die and succesfully curse others. Or torture them. One thing is to kill in power struggle and another thing is to be in cahoots with great evil.
And as for now there's no concrete evidence.
It's more shocking to him that Nok's gay and he himself won't be the king's relative than the queen trying to assassinate the crown prince -> tells everything about him.

I think he did, but Kyeong Jun doesn't know about the ghosts, right? Not only the three ghost but also the molesting ones.
In that conversation Nok's sure Eulsaeng was murdered but Kyeong Jun doesn't seem persuaded. He agrees "not everything is clear, but...". And in general his stance is that until the proof won't resurface, nothing can be done.
Nok was the one saying he heard the curse can backfire and the timing of queen's sickness but they don't throw accusations. Or speak like "omg it has to be her!" That part of the discussion ends with ordering Kyeong Jun to check who visited the queen late at night a few days ago.
He knows that the queen is actively out for Lee Nok's life. He went after Lee Nok in the forest 'cause he was told that assassin's had been sent to kill him.
He's gotta be, like, turbo homophobic to switch sides that fucking fast. He went from offering his baby sister's life to protect his "best friend" to going along with the queen's plans knowing she dabbles in shit far worse than some gay buttsex.
I think his gat is on a lil too tight, therefore all blood has been cutoff from his brain. Fucking loser.