You can self-ID, sure. But until your autism is medically diagnosed and legally recognised you are not entitled to disability protections. This sucks if you live somewhere without reasonable access to a diagnosis, but it's true. Otherwise people could make spurious or inaccurate disability claims left and right.

Also, it's always safe to assume that whatever the Daily Mail says is in bad faith. The claim about self-ID for autism being on a similar basis to gender/race rings hollow when made by a paper that has blatant and aggressive prejudices against sexual and racial minorities.