There are many ways that we can sort/categorise humans. We participate in both self imposed and externally imposed sorting/categorising. When it comes to pastimes and hobbies, we sort ourselves through opting to participate in specific events and activities. When it comes to jobs and studies, organisation will sort us according to our knowledge and skills. There are some legal restrictions on sorting by certain attributes (eg race, disability) when it comes to accessing employment, education, housing and provision of goods and services.
Humans can be sorted/categorised as being one of two sexes and in line with the traditional definition - a material, binary and immutable characteristic that applies to everyone. There are legal parameters relating to how and when this type of sorting should or should not be applied, in order to prevent discrimination.
Humans can be sorted/categorised by gender identity. There are many different gender identities, they can only be known/determined by each individual and having a gender identity is not universal. There are no specific legal protections relating to gender identity, but there are for gender re-assignment, which refers to people whose gender identity impacts on how they self classify their sex, leading to having or seeking a certificate that states they are the sex that they are not. There are legal parameters relating to how and when this type of sorting should or should not be applied, in order to prevent discrimination.
Having a legal document that claims someone who is the sex that they are not, based on their gender identity has significant ramification for that individual, for others who are of the sex that they are not but have legal documents stating they are, and for organisations who oversee the delivery of eduction, employment, housing and goods and services.
In light of the above, it is nonsense to suggest that the ability to obtain legal documents that declare you to be the sex you are not is of no-one's business other than the holder of the document.
The key laws that are relevant to this, that allows the creation of a legal fiction that people can be the opposite sex, are poorly constructed and because of this, are currently being challenged - in the courts, in parliament/politics, and in the media/on social media. There are conflicting/competing interests between different groups of people - essentially those who seek to ensure that sex remains a protected characteristic and is understood to be binary, immutable and independent of identity, and those who seek to reify gender identity and have it over-ride sex categories.
Many people can understand both sides of the argument and many/most hold strong views about which side is right. However, those who favour determining sex categories by natal sex tend to engage in substantive arguments. Those who favour gender identity trumping natal sex tend to focus on arguments based on perceived oppression hierarchies, claims that one group deserve kindness whilst ignoring what kindness to the other group requires, and also highlighting the harms to one group whilst overlooking, minimising or ignoring the harms to others.