The alignment spot on your character sheet is supposed to be a guideline, not a stopping block. Two characters who are both Chaotic Good may have completely different outlooks on what that actually means.
Most of the arguments on this topic are because people try to apply the alignment system to an objective viewpoint, when alignment is actually subjective and different for each and every person. As such, for each character, their alignment, while containing each of the nine alignments, will necessarily be different in a fundamental fashion. Because of this, no two characters will ever truly "share alignment", even if they both carry the same two word descriptors: their motivations differ, and as such their alignments will necessarily likewise differ, despite them carrying the same "alignment name."