I remember fuck-all about the story and characters' background, but generally remember their "factions", except the ball host's though. I'll probably be wrong somewhere
The MC's choice could be interpreted by the other characters as whose side she's on. Syl being unwilling to dance is due to thinking the MC disapproves of him, i.e. "unqualified." Derek might be anxious about dancing with her because (1) she is an "enemy" (2) it appearing to the public as siding/supporting with her, which is shown by his reaction to the crowd (3) the black bird fan superstition or symbolism (factions?) (4) and/or simply knowing her dancing skills being shit(?), he may have been referring to another event being "recreated".
The dice throwing can be interpreted by Clifford as her attempting to defy the gods or strong support of him/what he represents. This is complemented by him being able to land the 3, as if he's able to defy gods or help her succeed.
Something like that, maybe.