The only time I changed the hair color was at the beginning of the game. in creation I made Sammy a custom white-blonde. Never changed it otherwise. Once I completed the mission in question, if I had a necklace item, it soft locked and I could not change anything. So, I did a run where I picked a default character and speed ran to the mission not picking up anything or changing any appearance value. It worked just fine.
But then, to further test this, I did another new game and did the same speedrun without changing any appearance value but the only exception was I stopped and purchased the first necklace I came across from wandering around the stalls and it soft locked me again. So what happens is when you go to change appearance after the mission is over, it gets locked in the necklace accessory screen and you cannot cycle any of the other tabs.