Here's what I'm wondering: if they think this separate process is more reliable than traditional interviewing... why keep it a separate process rather than using it for everyone?
That's a self-adjusting question then. If the candidate finds a way to automate the boring part and/or make it faster, they've demonstrated at least two of the three Wall Criterion so that should be a +1 in their evaluation.
> The interviews often include tasks that traditional candidates would find boring and lots of repetition.
Intuitively this sounds like many programming tasks (I still like programming, but admit that many tasks in programming are quite repetitive) - thus good questions for neurotypical candidates, too.
While I admit I don't know the details, it seems unlikely to me that this process works the way you seem to be supposing it works, by somehow measuring bias and then correcting that out, such that it would yield incorrect results when applied to the wrong population. My suspicion is that it's more likely that it works by using processes that don't generate as much potentially biasing -- which is to say, irrelevant information -- in the first place. In which case it's just a better, less biased process in general.
Information can be irrelevant for evaluating autistics and relevant for allistics, too. Especially if you give autistic employees roles or support that obviates some of their common weaknesses - you'd still care about whether non-autistic applicants have those weaknesses.
If you're assigning them different roles, then that's actually a matter of what information is relevant for the role, not whether the applicant is autistic or not. If it's your support hypothesis, then the apparent relevance is due purely to the discontinuity in your "support function", so to speak. (Where some people need the support more than others, but only some are judged properly autistic and so receive it.) If it's a case where you can make the support available to everyone, with people just using less of it as needed, or if you can otherwise remove the discontinuity, then the problem goes away.