I read on irreversible damage that in the USA a human characteristic must be immutable in order to be included in human rights

That's a misapprehension. Not all characteristics covered by federal, state or local anti-discrimination laws in the US are immutable, meaning unchangeable over time. Disabilities can be acquired in life due to accidents, disease and disorders, disasters, war and assaults.

Lots of people who use wheelchairs, walkers and are legally blind were not born that way. In fact, the majority of people in the US who are disabled seem to fit that category, although the more we learn about genetics it might be that people who develop various disabilities over the course of life due to disease, disorders or other medical conditions have a genetic predisposition to them.

Similarly, pregnancy is temporary, as is maternity in the way it's defined in law - yet protections are in place prohibiting discrimination on these grounds in certain settings.

Also, over the course of history some medical conditions that qualify as disabling per the law and once seemed unchangeable have become manageable or even curable, the way it's happened with cancers and HIV that once were fatal. Many people with severe motor and speech disabilities from stroke that left them helpless initially can eventually recover from them to a greater or lesser extent (as the Patricia Neal case showed). Some forms of once disabling and fatal genetic primary immune deficiency such as SCID (severe combined immune deficiency, or what used to be known as "bubble boy disease") that kids are born with are curable if bone marrow transplants are done before 24 months. Advances in smart prosthetics now means some people who've long been without limb function might be able to regain function.

Religious creed, also protected under US anti-discrimination statutes, is not immutable, either. Many people with deeply-held religious beliefs are converts; they were not born into their religion.

One of the most famous religious discrimination cases in the US was the landmark lawsuit of Muhammed Ali Cassius Clay against the US government (Cassius Clay vs. United States) over the Selective Service not granting Ail conscientious objector status based on his being a Muslim. Ali only became an adherent of Islam in adulthood; AFAIK, he was raised as a Christian. BTW, the US Supreme Court ruled in Ali's favor in that case.

In some jurisdictions in the US - such as CT, CA, NYC - legal protections are already in place for "gender identity" and "gender expression" - neither of which, as we all know, are immutable. Obama during his second term reinterpreted US federal anti-discrimination law to give "gender identity" more status than biological sex in determining eligibility for participation in female school sports, and which toilets and locker rooms students use - as well as for placement in federally-funded shelters. States like CT and CA have passed laws saying convicted criminals must be placed in prison based on their "gender identity," not their sex. In NYC, it's now a civil offense with a fine of up to $250K for a landlord or business operator to "misgender" someone who is trans, enby, whatever.