So according to a Christian standpoint, they would be heretics.
Your non-specific claim is not actually a quote.
Where does "the Bible say" that there should be no religious leaders? Paul, James, Peter, Jerry Falwell, Jim Bakker, former Presidential Candidate Pat Roberston, all have made statements about God and all have been followed and admired as spiritual leaders by Christians of specific denominations.
And the head of the Church of England is still a particular Bishop, under the Queen.
Now: before you go into that whole "the Pope claims to be infallible" thing, that's a misunderstood idea that is frequently misapplied in this argument. The Pope claims to speak for God, sure, but that's not unique to Catholicism, and I don't think it is heretical according to Christianity as a rule. Paul claimed to speak for God, and is personally responsible for most of mainstream Christian belief and practice.
I got my own problems with Catholics, but I don't see anything hertical about the way they run their religion.
"all the other stuff in the mix' I attribute to allowing their faith to change over time and allowing for the idea of continued revelation. It's just as crazy, IMO, as "God does not talk to people ever, never ever, but come to chuch and hear the Word of God!"
My personal favorite tactic when dealing with Fundamentalist Christians is not so much to know more than they do, but to ask for backup of everything they say. Like "Where's it say this?" or "How do you know that?" You find pretty quick that most folk are talking through their asses about what they know about their own religion. Then at some point I tell them I don't like religion, so they can say "I am not religious; I have a personal relationship with God and the Bible." I am then free to offer the one-two punch: "if everything you say comes from personal study, and not from religion, then how come you don't know where to find it?"
Nothing pisses off a Fundamentalist more than having it proven to him that he's religious.