Well, would a Turing test be as meaningful if you introduced, beforehand and for this specific case, strong evidence or suspicions that the other party is probably an experimental conversation simulator?

I think it's fair to assume the same implicit conditionals for ideological Turing tests (the person says it with sufficient conditions, the "tester" doesn't have any previous evidence for this specific situation, etc.) as for vanilla Turing tests.

In that way, I would conduct an ideological Turing test by having both parties meet for the first time, introduce themselves both as members of the ideology (perhaps implicitly), and then executing the behavior or saying the statement that needs to pass the test, for the kind of cases you described.

I figure it's pretty much all into how "hard" or "strict" you want to make the test.