Immutability is the inability of a thing to be changed. For example, it is impossible to change a dog into a cat. Likewise, it is impossible to change one's race, although with makeup or plastic surgery has made it possible to alter one's racial appearance. The immutability of membership in a group is an important consideration in determining the level of scrutiny given to a law against that group under the Equal Protection Clause.
There is some debate over whether a "sex-change" operation is valid as regards whether one's sex is immutable or not.
There has been much debate over whether homosexuality is immutable. Often the argument is made that it's either genetically determined (and thus immutable), or that it is entirely a matter of choice. Given this dichotomy, the premise that "I didn't choose to be gay" yields the conclusion that it must be genetically determined. However, the search for a "gay gene" has proved elusive. Many others, including most scientists, have a much less 'black and white' view. They propose that it is determined by a complex interaction of many factors, some of which could be genetic, but probably also include psychological, environmental and cognitive factors, and is shaped at a very early age.
Simon LeVay wrote: "It's important to stress what I didn't find. I did not prove that homosexuality is genetic, or find a genetic cause for being gay. I didn't show that gay men are born that way, the most common mistake people make in interpreting my work. Nor did I locate a gay center in the brain. ... Since I look at adult brains, we don't know if the differences I found were there at birth or if they appeared later."
- Byrd, A. Dean, Shirley E. Cox, and Jeffrey W. Robinson (May 27, 2001), Homosexuality: The Innate-Immutability Argument Finds No Basis in Science. Salt Lake Tribune