No, the test itself is definitely the problem. Regardless of whether you believe a personality type test can be effective, the MBTI is particularly and provably ineffective in just about every measurable way:

It’s not reliable. It has terrible test-retest reliability. If I’m X personality type, I shouldn’t test as X type one time, and Y type the next, and Z 6 months laters.

It’s not predictive. If a personality test accurately judges someone, it should mean you now know something about someone’s behaviours, and can extrapolate that forwards and predict behavioural trends. MBTI does not.

It fundamentally doesn’t match the data. MBTI relies upon the idea that people fall neatly into binary buckets (introverted vs extroverted, thinking vs feeling, etc). But the majority of people don’t, and test with MBTI scores close to the line the test draws, following a normal distribution. So the line separating two sides of a bell curve ends up being arbitrary.

And finally, it’s pushed very hard by the Myers-Briggs foundation, and not at all by independent scientific bodies. copying straight from wikipedia:

Most of the research supporting the MBTI’s validity has been produced by the Center for Applications of Psychological Type, an organization run by the Myers–Briggs Foundation, and published in the center’s own journal, the Journal of Psychological Type (JPT),

I’m only responding to the assertion that asking “what cis women think about playing trans women” is morally equivalent to asking racists whether they want to play against black people.

But I think this part is where the disconnect is happening. Before this decision, cis women and trans women were both components of women’s chess. The act of conferring with only a subset of that group implies that the other does not fall into that category. Relying only on the majority group’s opinion on the status of the minority group is itself an assumption that one of the groups inherently belongs less than the other.

Nah, I don’t buy it. The assumption with this line of thinking is that trans women don’t inherently belong to that class of participation. The majority of a group (cis women) do not get to unilaterally decide who is/is not a part of the greater group (women).

If someone proposed a restricted class limited to PoC, it would be entirely appropriate to ask PoC what they think about the proposal.

But following this analogy through, you’re not asking all PoC. You’re asking the majority of the subset (for example, black participants) whether a minority of the subset (for example, Asian participants) should be allowed to participate or not.

In this case, the organizers of these tournaments are picking and choosing their own definitions for who qualify as “women” and listening only to those opinions. The decision is already made, and pointing to the remainder to justify the decision is working backwards from that conclusion.