It is that rotten core that we are to avoid. Not everything pagans do in worship is inherently evil. They go to a temple. These are customs of pagans, and they may do them as they are sacrificing people. What is critical to God is how they sing, how they behave in their temples, how they pray and to whom they pray.
People can corrupt and misuse anything.
Paganism's polytheism and immorality are what disturbs God. Polytheism and immorality are the pagan way. Israel was not to adapt that way in its worship of God. In trying to make a right judgment, sometimes Christians label others as pagan without understanding what a pagan is. By anachronistically imposing ancient settings on modern venues, we falsely condemn Christian customs.