Ting-Ting, Su, and Mei had their feet binded
In "Like Other Girls", Ting-Ting, Mei, and Su remove their shoes (which they deem as "pinchy") and spend the rest of the song barefoot. In history, it was a Chinese custom of breaking and/or tightly binding the feet of young girls in order to change their shape and size, resulting in lotus feet. As a result, it would make it rather painful to walk in proper shoes. The princesses themselves might have had their feet binded at one point before the events of the film, so this could be a theoretical cause as to why they want to ditch their shoes.
- I don't believe they have any problems walking, which they certainly would have if they had their feet bound.
Ting-Ting, Su, and Mei do not have the same mother.
A comment from the first film reveals the emperor has concubines, in which case it seems more likely than not that the emperor would make sure he had lots of heirs. While it was a Hun who said this, the Huns were at least well-versed enough to successfully infiltrate a parade.