There was no 'recategorisation of transgender identity' in the DSM5.
This is an outline of the changes made to the previous diagnosis of gender identity disorder (GID) in DSM5 and the rationale for them as outlined by Zucker et al (2013).
In DSM-IV GID was placed in the Sexual and Gender Identity Disorders, even though there was little or no theoretical overlap between GID and sexual disorders. As Zucker et al explain "The placement of these three diagnostic classes in the same section in DSM-IV was probably influenced by several considerations, including clinical utility (e.g., that clinicians and researchers who study these phenomena tend to affiliate at common scientific meetings, tend to publish in the same periodicals, and probably have at least some familiarity with all of the conditions more so than clinicians and researchers who specialize in other areas of interest to psychiatry)."
However, consultation lead to a decision to separate gender dysphoria from sexual disorder to reduce stigma. Likewise the title was changed from GID to gender dysphoria (GD) to focus on distress rather than identity and reduce stigma. It is a myth that under DSM-IV, simply having a 'trans identity' was considered a disorder, but under DSM5 only having dysphoria is. Under DSMIV there was also a requirement for 'evidence of clinically significant distress or impairment in social, occupational, or other important areas of functioning' to make the diagnosis. Having a trans identity or being 'gender variant' without dysphoria was not sufficient. In other words, the name was changed but the underlying theory and the basis for diagnosis receive only minor revision.
The narrative that 'trans identity' was declassified as being a disorder in a manner parallel to homosexuality is pushed by activists for political reasons. As Singal states '
"One of the main warning signs I look for when determining whether a given outlet is trustworthy on the subject of youth GD is whether it disseminates activist talking points without fact-checking them. This is one such talking point: the idea that in the DSM-IV, simply “being trans” and/or acting in a gender nonconforming way was considered a mental disorder, but then in the DSM-5, this injustice was rectified'."