Is it permissible to listen to Christian rap music?
All Christians enjoy liberty in all amoral matters (i.e., matters that are not moral or immoral). Music style is an amoral choice. No style of music is good nor bad. On the other hand, the lyrics in the music we choose do matter, since words can be either edifying or destructive.
If the music you follow has edifying lyrics (i.e., they are wholesome and glorifying to the Lord), then the musical style is irrelevant. On the other hand, if the words in our music are destructive, profane or blasphemous, we are sinning to frequent such things, as Paul says:
So long as we do not feed ourselves a diet of worldly thought and depravity by our choices in entertainment, then we do not sin in our preferences. But we must remain diligent and discerning, since the enemy is always working to introduce new lies into the culture when we aren’t watching.