Here are the ingredients in AQUAPHOR:
Petrolatum (Vaseline), Mineral Oil (Paraffinum Liquidum), Ceresin, Lanolin Alcohol, Panthenol, Glycerin, Bisabolol (L-Alpha)
While these ingredients are much more mild than the usual chemical laden ointments and creams, there are 2 that are of at least some concern: Mineral Oil and Lanolin Alcohol. Both are listed as human skin toxicants potentially causing allergies/immunotoxicity.
I know for a fact that mineral oil can cause an allergic reaction, because my skin is very senstitive to mineral oil and reacts badly to it. I have no personal issue with lanolin or lanolin alcohol, but there are plenty of people who do. People who have a wool sensitivity/allergy usually have the same reaction to lanolin. This can be very severe in some people.
Bottom line, while Aquaphor might be well tolerated by many people, some people will have a bad reaction to it.
Another alternative would be "Un Petroleum Jelly" by Alba. It is made from only natural plant oils and waxes (contains no petroleum products). It has a texture very similar to Vaseline, but is made from natural ingredients. It sticks to the lips well because it has some beeswax in it, and also castor oil which is naturally a bit sticky.
Between these two products (Aquaphor and Alba Un-Petroleum Jelly), the Un-Petroleum Jelly is the more natural product.
Alba Un-Petroleum Jelly ingredients:
Ricinus communis (castor) seed oil, cocos nucifera (coconut) oil, beeswax, hydrogenated castor oil, tocopheryl acetate and tocopherol (Vitamin E).