There's been a long debate about how one should refer to Autistic people (and people with disabilities in general). It's a heated affair with strong advocates for either side. On one side Autistics are incensed that people would refer to them in a way that separates their Autistic essence from their identity on the other parents, disability advocates and researchers want to acknowledge the individual's humanity first and separate it from the disability which brings with it challenges and potential discrimination. Of course there is overlap with people in the categories I've mentioned belonging to the opposite camp as well. I guess the message I want to convey here is that person-centred language is not appropriate if the person being referred to considers what is medically defined as their disability as a core part of who they are and how they perceive the world. To use person-centred language in this context is to accept only part of the person, dismissing a key part of them as being inferior.
I find it interesting that the groups within the disability community which vocally object to the use of person-first language are those for which their disability fundamentally changes the way they see the world: The Autistic community, the Deaf community and the Blind community. It's possible to separate a missing limb from who you are internally as a person, not so the very nature of your experience of the world and everything in it. Perhaps the use of person-first language is valid outside of these parameters but when one sees the world fundamentally different it contributes significantly to who you are and how you perceive and interact with your world.
If you struggle with the concept or aren't sure about it I would encourage you to read an article by Oliver Sacks, the world-renowned psychiatrist best known for his books of interesting case studies such as 'The Man Who Mistook His Wife For A Hat'. He once wrote about a man named Virgil who had lost his sight early in childhood and gained the ability to "see" in his 50's. What might seem like a miracle, actually proved to be very difficult for him. His brain and how he perceived the world had great difficulty adjusting to this new bombardment of visual stimuli. It made his life harder to navigate, not easier. I think this article provides interesting food for thought which takes the 'separation of disability and identity' , 'cure' and 'normalization' arguments out of the black and white and demonstrates the shades of grey that defy the assumptions people tend to make. The article can be found here: http://www.willamette.edu/~mstewart/whatdoesitmean2see.pdf
Working out and accepting who we are is a massive part of life and happiness. How much harder is that process if people are constantly telling you that who you are isn't good enough, and worse that you're always going to be that way no matter how hard you try? This is where the negative stigma and deficit based perceptions of autism can be damaging. Autistics start out lower on the ladder of social skill and acceptability than most people and have a long way to climb to try and reach a point where they can interact successfully enough with the world around them to be accepted.
If they are constantly told to correct their behaviour or that they are somehow wrong that contributes to low self-esteem and anxiety which can make it even more difficult to be motivated to keep trying and learning. Feeling powerless or unheard also doesn't help. Is this about blame - no. This is about respect. This is about drawing a line in the sand and saying who are we, that is society, to say that one person is more valuable than another? Who are we to say that one has more right to have an opinion than another, particularly about things which directly affect them and those like them? Who are we to say that there is one "normal" way of being and anything different to that is unequivocally and irrevocably less? At the core of the idea of "cure" is the concept that someone is defective unless they are fixed.
In French the way you ask for someone's name is effectively "what do you call yourself?". I think we have the right to identify and introduce ourselves how we see fit. If someone says I am Autistic, respect it. If they say I am a person with autism, respect that too. But don't let convention get in the way of someone's identity. Have a default mode sure, but respect the fact that people have a way they want to identify themselves and be acknowledged. If someone doesn't refer to the fact they're Autistic as a disability, don't refer to it as one around them. Be respectful, be accepting and be empowering of that individual. Frame them by their strengths and not just an endless list of things that need fixing for them to be worthy of inclusion. That's assimilation not inclusion.
If you're still not sure in a given situation ask yourself does your use of person-first language make the person feel valued? If that is your intention behind using person-first language then it is a natural progression to be open to changing your language in order to make the person you're referring to feel accepted. Words are highly contextual. They are powerful. They can make people feel included or marginalized, valued or patronized.
If your intention is to accept someone then use your words in a way they find accepting. Accepting of who they are, how they identify themselves and how they see the world.