Difficulties with mental health services
Autistic people often face difficulties when accessing mental health services, either due to not knowing they're autistic themselves and mental health providers not recognising it either, or because they face hurdles that are difficult to overcome since they are primarily designed for allistic patients.
Misdiagnosis
It is very common for late-diagnosed autistic people to have been diagnosed with other mental health disorders prior to discovering that they are autistic. Many mental health disorders are well-known to frequently cooccur with autism, including but not limited to mood disorders like depression, anxiety disorders, stress disorders like C-PTSD, and more (cite studies). Personality disorders, especially borderline personality disorder (BPD), may also be diagnosed, and while you may fit the diagnostic criteria for both BPD and autism, BPD may or may not have been a misdiagnosis. Autistic people, especially women, are at a heightened risk of being inaccurately diagnosed with BPD, without an accurate assessment being performed.
Stereotypes & lack of education among professionals
It is common for mental health professionals to have beliefs about autism which are outdated and not fully informed. They may not be able to fully appreciate that autism is a spectrum, so presentations can vary widely among autistic people. Unfortunately, it is not unheard of for people to be denied diagnosis on the basis of things like having the ability to make eye contact or having a job, which speaks to harmful stereotypes about autistic people. If a professional tells you that you "can't" be autistic for one specific reason, they are likely misinformed about autism.
Difficulty accessing diagnostic services
This varies greatly by country, but there are many common barriers, including the above, as there is a lack of professionals who are accurately educated about autism.
Dangers of unrecognised autism
{examples of all the bad things that can happen when mental health service providers don't know the patient is autistic, such as wrong treatments or under-/overestimating the severeness of suffering, due to misreading tone of voice or body language}
When autism is not recognized, the autistic person could end up with a misdiagnosis and be put on medications/therapies that do more harm than good. Common misdiagnoses seem to be Bipolar Disorder and Borderline Personality Disorder.