I have not consulted Ron Haver's book on the making of A STAR IS BORN, but if I had to guess about Garland's changing hair styles in the beginning of the film....it would be that it's a fact that there were numerous reshoots of scenes (due to switching to Cinemascope, Garland's volatility) and those reshoots probably account for the fact that the hair does not match from scene to scene. It probably took too long to redo her hair to make it match if they were doing a reshoot.
Your insisting that this is some sort of major flaw reminds me of a story Shelley Winters used to tell about the shooting of A PLACE IN THE SUN. After completing a scene, Winters realized she was wearing brown shoes, not white, as she had been in the previous scene. She went to director George Stevens, full of fear, and confessed that she had not spotted the potential error in continuity. Stevens responded, "Shelley, if they start looking at your shoes, we've lost the game."