As an example, let's use the song "The Black Parade" as an example. The song speaks to some parallels to Trinitarian references and talks somewhat about the songwriters "faith" (Gerard Way). I'm not too clear on what his faith is about, or whether he considers himself a follower of Christ, but there are definitely some Christian influence that impacts this song. On the surface, Way sounds like someone who is struggling with understanding death and its implications. Anyways, the song itself has some interesting themes to ponder and musically speaking, the musical arrangement itself is crafted quite EPIC-ly in the vein of Queen's "Bohemian Rhapsody" or Radiohead's "Paranoid Android".
Overall, I'm sure MCR and other bands like them have their own personal issues. They have probably written some terrible songs or songs that just perpetuate a sense of depression or hopelessness. But on the other hand, they've probably written some songs that have boosted some people's spirits (especially in some forums I've read). In terms of the question on whether this kind of music is "permissible" to listen to, I'll point to the Apostle Paul:
"Everything is permissible for me"—but not everything is beneficial. "Everything is permissible for me"—but I will not be mastered by anything." - 1 Corinthians 6:12
When we follow Christ and live by His word, we will see things differently, through His eyes. Music and culture isn't neutral and should be waded through carefully. Questions in light of this verse: "is this song beneficial to me?" or "does this music master me or manipulate me?". Overall, if we truly follow Christ, we'll ask these kinds of questions before we take stances based on preference.
Also read this answer for some more information on discernment in our culture. Click HERE.
[answered by Pastor Shu-Ling Lee, English Congregation Worship Pastor]
