I personally feel that gender is a social construct. Also, sorry for any typos, I'm using a phone to type this.
I've seen studies that show that males and females have brains that are "wired" differently (certain parts of the brain are larger in the average male, other parts are larger in the average female). These sorts of studies are often the "objective" evidence that research relating to trans people will cite to justify the subjective notion that trans people have the "wrong" brain for their body. For example, a trans woman might have a brain more closely resembling the average biological female, and a trans man might have a brain more closely resembling a biological male.
However, this entire viewpoint still weighs the data based on a socially-constructed, binary system of "gender." It is unscientific to seriously assert that there are two types of brains (male and female). Brain "types" fall under a huge spectrum; any connection between a person's *** and that ***'s "average" brain type is obviously a loose correlation at best.
I believe this problem is further exasperated by the contradictory nature of gender "ideals." It is very rare that a person will "match" all, or even most, of the standards of their ***'s supposed gender. However, failure to match these standards, or more closely matching the "gender" of the opposite ***, hardly proves that one's "true self," beneath their mismatched exterior, was born to be the opposite gender. Rather, such cases merely highlight the toxic, manufactured, and ultimately harmful baseless binary concept of gender.
Certainly, I don't believe that arbitrary exterior factors such as wearing makeup, dresses, or baggy jeans truly transform a person to "fit" their "inner self"; these aethetics have no inherent gender other than what society places on them. They might serve as a crude way of communicating to the world that one doesn't identify with the stereotypes surrounding one's ***, but no person is truly born with a "gender." The concept of gender is simply obsolete.