Birds do not have capsaicin receptors, so don't detect 'spicy hot' stuff, like mustard or hot sauce.
That's why red pepper flakes works in wild bird feeder to keep squirrels and other mammals away.
Have read way too many stories about folks feeding empty half shells to their chickens, with no resultant egg eating. Guy I used to chicken sit for showed me to take any cracked eggs and bust them on the floor of the coop, those birds also never tried to eat any intact eggs. Have also had my birds eat weak and thus broken eggs in the nest but not touch solid shelled eggs.