Yes.
Sex is not a single attribute on a human, but a collection of attributes expressed through primary and secondary sexual characteristics on a human. In most (but not all) people, those characteristics align as one of the two major sex classes (male and female).
Through medical intervention, such as through the use of hormones causing changes to the endocrine, or surgical intervention on primary sexual characteristics, then it is possible to alter your expressed characteristics to align a sex class different than the one you are born with. Many trans people undertake this, or intend to. Not all trans people do, and medical transition to change sex is not a requirement of being trans. This is what we mean when we say we change sex.
There is also a significantly more binary “legal” definition of sex which is recognised by the British legal system. In cases where someone’s sexual characteristics are more ambiguous (intersex), a sex is assigned to them at birth. For trans people, where through medical intervention we change our sexual characteristics, the legal system has for over 20 years recognised that because of the existance of trans people who medically transition, it provides a process for updating your legal documentation. Many other countries also allow you to do this, with different levels of bureaucracy.
So yes, sex can be changed. Both physically and legally.
If you’d like to read more about why I felt a need to state what should be obvious, read on…
There is a movement, linked to far-right religious movements in the USA, which is attempting to redefine sex as not being based purely on observed sexual characteristics, but instead are using a definition of sex as purely binary based on the size of produced gametes. This is a much less useful definition from a medical standpoint, and not widely accepted as it fails to deal with ambiguous cases, and makes it harder to determine someone’s sex as establishing what internal reproductive system someone has is a lot harder than observing their sexual charactertistics.
This movement claims that this definition is part of the “gender critical” belief system. There is a significant overlap between those who claim to hold this belief, and those who behave in transphobic ways, such as campaigning to reduce legal protections for trans people, undertake public harassment of trans people (as a publicly visible trans person, I have been on the receiving end of several hate campaigns by gender critical campaign groups) and ultimately, I believe, seek to force us back into the closet through reducing acceptance of trans people, to eliminate us from society.
In the UK, a court case rejected the argument that these beliefs were valid, but this decision was overturned in a higher court of law, resulting in this view winning legal protection as a philosophical belief system similar to a religion. I believe this decision was a mistake, and gender critical beliefs are nothing more than a legal fiction used to justify transphobia, with this redefinition of sex a pseudo-academic invention to attempt to legitimise this. In holding this view, I have been accused of being an intolerant bigot. Sadly this movement is seeing some success in their attempt to push a redefinition of sex based on this legal ruling.
It is crucial that you reject the attempt to redefine sex, and to not accept intolerance towards trans people. You do not have to tolerate an intolerance movement, and it is not intolerant to reject intolerance.