Would I be sinful if I cut ties with my friend who delays prayers and listens to music, despite her insistence that God will forgive her, and despite my repeated advice to her?

For your friend to insist on committing sins, and to insist that Allah will forgive her, this is a form of delusion (ightirar) mentioned in the verse: "And let no deceiver deceive you concerning Allah" [Fatir: 43], and it is a form of delusion for a person to commit sins and wish for forgiveness. We advise you to continue counseling her with encouragement (targhib) and deterrence (tarhib), and to give her beneficial audio lectures. And those who have a relationship with her should advise her in the best manner, so that she might return [to righteousness]. As for shunning her, this depends on the benefit (maslahah); if you predominantly believe that shunning her will deter her, then do so.