If a judge hands down a decision to give a defendant custody based on a child being possibly autistic via therapist speculation without the child being officially tested for autism is this good grounds for a plaintiff to appeal?
To reframe the question, what you are really asking is what evidence considered by a trial court is sufficient to support its custody decision on appeal.
Courts have broad discretion to enter custody orders that do not hinge on a formal diagnosis of any particular mental health conditions, and their decisions are reviewed on appeal for abuse of discretion.
The trial court's factual findings will be upheld if there is any admissible evidence that was presented at the custody hearing that supports the trial court's findings of fact. The overall decision will be upheld if any reasonable judge who made the findings of fact made by the trial court that are supported by admissible evidence that was offered at trial could reach the same conclusion (whether or not the appellate judges would do so if they were first to encounter the case in the trial court).
Also, an appeals court can only consider issues that the trial judge had an opportunity to consider because the party seeking to appeal "preserved" that issue by asking the judge to make a ruling or consider a legal issue in a custody hearing, and the judge didn't do what the person appealing asked.
If an objection was made in the trial court to having the therapist making an expert opinion on whether or not the child had autism, that expert opinion could be subject to an appeal, and the person bringing the appeal on that issue might prevail on that issue. But that wouldn't be very helpful because the judge wasn't asked to determine whether or not the child had autism. It would be "harmless error" and would not be a ground for overturning the custody decision. (And, if no objection was raised in the custody hearing, the issue is not a valid subject of an appeal at all, even if the judge's decision was incorrect.)
Even if the therapist's expert opinion on an autism diagnosis was wrong or improper, the non-expert testimony about a child by a therapist could easily support the judge's decision and would usually be admissible as evidence.
The question the judge had to decide was hearing the facts presented at the custody hearing, what custody arrangements should be put in place for the child, something that could be defensible on appeal even if the judge was wrong to accept an autism diagnosis.
An appeal of that issue in a custody case is very unlikely to be successful, although there could be other nuances of the ruling that might present an issue for a valid appeal.