KoC can't get MoN >.<

There are a ton of quests that aren't working for Cygnus right now (Jane and Wild Boar, Arwen's glass shoe, Sauna robe,etc etc.) because Nexon didn't put Cygnus Job IDs in for the quests that had lists of Job IDs (this is usually done to exclude Beginners.) I suspect there's a similar problem here, unless they specifically say something about you being a cygnus when you attempt entry. If it does, I'd like to see a SS of this because it would be rather surprising. I don't see any reason why they'd exclude them from it.

The door said exactly what the guy under says.

No.

Jack Barricade specifically says.

"You are a member of the Cygnus Knights, you do not belong here."

I think it's intentional.