In evolution, there exists the transition of unicellular organisms to the multicellular organisms we call humans.

When bodies of organisms transition to such an extent, how can you say sex is unchangeable and one can not transition to become the opposite sex?

You don't seem to understand the difference between evolution of species and the aging of individual organisms. Two entirely different things.

From the moment of fertilization through gestation, birth, childhood, adolescence, adulthood, old age until and after death, each and every plant, animal and human being will have exactly the same DNA and sex chromosomes.

Yes, our bodies all make new cells constantly to replace all the cells that aren't constantly dying off. We each make billions of new cells each day. But every one of an individual's own cells - new, old, dead or yet to be made -still will always have the exact same DNA and sex chromosomes.

In four different groups of humans, some cells with different DNA and sex chromosomes might also be present in an individual's body: the very few people who have the extremely rare conditions known as mosaicism and chimerism (and the mechanisms for why this happens is clear); currently pregnant women; and some women who have been pregnant in the past, particularly those of us who carried fetuses to term or past a certain point of gestation.

Sometimes some women retain some fetal cells from our children even years after we've given birth to them. But because some women carry some leftover cells from our sons in some parts of our bodies after birth doesn't mean we have changed our sex. It's very easy to distinguish between cells that have a woman's own DNA and sex chromosomes and fetal cells that might have been left in her body from her son(s) and/or daughter(s).

Sex is part of the body, the body changes every second of everyday, and so it follows that sex which is a part of the ever changing body can change with it.

In humans and many other animals, sex characteristics change over the course of each individual organism's development and aging. But our sex does not.

Many cats and dogs are spayed or castrated, which is sometimes referred to "neutered." This doesn't turn a male dog into a female one or a female cat into a male one, nor does it make them no sex, either.

Whether a male or female human is 1 day or 100 years old, their sex remains fixed. Sex characteristics change, not a person's sex. Just the way human skin remains human skin whether it's on a newborn or a very old person.

When someone has plastic surgery, you don't say their body didn't change.

When someone dyes their hair, you don't say the hair color didn't change.

When someone tans, you don't say the skin color didn't change.

But when someone takes hormones, and undergoes surgery to be given a neopenis or a neovagina, you go on the prolonged back and forth that the sex didn't change event hough the body itself changed

The people in all your examples have changed their appearance to varying degrees, and the persons in your last example who've had "bottom surgeries" have altered how their urinary anatomy and parts of their genitals function in certain limited respects. But none of them has changed sex.

The trans persons in your last example have made cosmetic changes to their bodies through surgeries and use of chemicals just as the people in the preceding three examples have.

The surgeries and chemical treatments trans people get result in changes akin to using hair dye, getting a nose job or facelift, tanning the skin (or alternatively, bleaching the skin). Or to add some additional relevant examples, they are similar to getting dental crowns, veneers, fillings or implants; to getting a skin or bone graft; to having an organ such as the appendix, gall bladder, spleen, uterus, tonsil or other body parts such as moles, tumors and facial hair removed; or to getting a surgically-attached prothesis, a pacemaker or stent. Thank you for making this so clear!