I do think those who refuse to look at or acknowledge the spiritual nature, their own spiritual nature are indeed spiritually dead (though not necessarily hell bound) and useless for sure when it comes to serving God. Of course, unfortunately they likely don't believe in God so they view it as nonsense.
I think when it comes to worshipping other gods, as I said, there is one God. But people can make idols out of a lot of things, and they can almost worship them. Not necessarily in the sense of praying to them, but in honoring them, in becoming obsessed or overly preoccupied with them. Certainly too any other religions... well it's important to remember that while as a Christian I certainly believe other religions are incomplete, lacking, or even lies, it's important to remember that the commandment not to worship other gods went to the children of Israel and to believers today. This is not to say that people of other religions are okay or saved. It's to say that God is the judge and ignorance in and of itself is not a sin.
Basically though I believe it would involve giving reverence to, if you will, something other than God... be that another religion, be it some religious figure or so called god, or be that some fleshly hang up that keeps one of God's children who claims to love Him from actually showing or exhibiting that love and more to the point, where that other "thing" or "god" becomes more important to them than their own Heavenly Father.