There are a few basic principles that apply, over which "black and white thinking" Christians seem to get "spiritual indigestion".
One of them is that God can use whatever he chooses to use, for example: many "evangelists" who turned out to be big liars may have been instrumental in many souls saved. Bar room songs have been turned into hymns.
Another is that NONE of us, no matter how sound in doctrine, quite understand what God has done for us; none of us has it quite right. No way we can "sound the depths of love divine", nor the horror that sin is, nor the purity and justice and mercy of God. Many a coherent thought that tugs at the heart and has the feel of truth is assumed to BE true, that is not. (I don't say that to justify those you refer to, but...)
Another thought concerns a quote I can't seem to find that has in the last many years meant a lot to me; it goes something like this: "Nobody can in praise or worship improve on what God has said about himself".
The human heart, I have found out, no matter how emotionally exulting or full of praise (or heartfelt repentance, even), can be trusted, including, and maybe specially, my own. But God, and the Word of God, has never let me down.