I started referring to myself as an Autistic person some time before I even knew there was a convention with disability for referring to those with disabilities as “persons with X”.
I think it just seemed to make sense to me. I have also seen how an autistic friend struggling with her difficulties used to talk about how “her autism” affected her and this was affecting her self-esteem.
It’s intuitive that I’m an Autistic person and “autism” is fundamental to who I am and how I process the world. Internally if you separate the autism and connect it to all your difficulties, you set up an unresolvable tension in your own sense of self.
When Autism has been adopted by those who actually are Autistic, it ceases to be the original term indicating a disability. Autism is not a disability as such, but it is a difference that can be hard for non-autistics to understand. I can see that putting autism in a “Person with autism” context means that whoever you apply it to cannot accept themselves as Autistic properly.
So that’s why I would continue to use this way of referring to myself and suggest it is a better way of using language. Autistic people really need to be able to move beyond thinking of autism as a “problem”, and it does not help to have an inappropriate convention imposed from a “difficult condition” context.