A chicken’s egg is made up of different proteins. The proteins change depending on if the eggs are raw or whether they are cooked. Typically a consumer can separate out most of the yolk from the white at home and there are different egg products available that are either yolk or white. Since we can limit the ingestion of either yolk or white, those who are intolerant of eggs still hope be able to consume eggs. This brings up the question of which is the worse offender, the yolk or the white?
Typically there seems to be an increased number of individuals who are allergic to the white of an egg so it may hold true that those intolerant to eggs may be by and large more intolerant to the whites than the yolks. There are over 40 proteins in the white with the yolk not having anywhere near as many. It is the proteins that cause the allergic reactions that involve the immune system so considering it may very well be the proteins causing the intolerance issues is not a stretch of the imagination at all.
So if there is a need or intense desire to consume eggs though there may be an intolerance to consider, then eliminating the whites of eggs first to determine if that is the cause is okay.