Self-diagnosis (or self-dx) is generally accepted in the Autistic community because often it is both hard and expensive to get a formal diagnosis. In many cases, an individual may decide it isn't worth pursuing. Many people self-dx after immersing themselves in online Autistic communities, thoroughly researching the available literature, and engaging in intensive self-reflection (something Autistics tend to do a lot of).
Barriers to receiving a formal diagnosis include: sexism against women who are recognised as Autistic, racism, poverty, lack of access to healthcare, lack of access to queer-accepting healthcare, and the fact that many doctors refuse to diagnose adults who were not diagnosed in childhood.
Some people may also avoid seeking a formal diagnosis due to the stigma of having an autism diagnosis on their medical record. Consequences vary from country to country, but for example, autism diagnoses have been used to deny child custody, access to medical care, entrance to some countries, and general autonomy.
Note, some autists on their self-dx journey may be hesitant to "diagnose" themselves, viewing diagnosis as a word that denotes a clinical determination. In this case the term "self-assessment" may be useful. Laypeople as well as clinicians can and do assess their own traits, struggles, needs and strengths; the Autistic community affirms that people are experts on their own experiences and qualified to draw conclusions about who they are.
Embrace Autism Self-Diagnostic Tests