Warhammer Chaos alignment does not really match D&D alignments.
First, Warhammer Chaos is about an intrusion from immanently hostile and immanently incompatible far realm. Serving Chaos means gradual descent to physical and mental abyss of otherness.
Four great powers of Chaos represent certain correlations to human traits, however they merely weaponize them for the purpose of their recruitment drive.
That's why ultimately Chaos worshippers are separate, different and not really the same as worshippers of normal gods. A Bhaalite may be a brutal murderer but their evil is humane evil. A Slaaneshite evil is closer to that of Cthulhu cultist... with high probability of physical changes.