I find it highly plausible that an ideologies own arguments could be interpreted as satire if there were impostor-suspicion (which the test would cause).

I was aware (though i didn't think it through to that it might be interpreted as satire). But the ideological Turing test has been described as a conversation with six candidates, so in this thought experiment the five other feminists would also be suspected, not just the one we're testing. (The readers i understand to initially have no reason to particularly suspect any of the six more than any other.)

And in a way, that one feminist doesn't differ from the other five. Indeed she could have equally well be selected as one of the five instead. (It is unclear to me whether we would tell the tested feminist that she is being tested.)

I feel like I can't say this without it being interpreted as a jab at feminism,

Well, personally, i love good jabs at feminism! And "good" here does not necessitate "nice".

but I think such a test where you arouse a bit of suspicion and then play back some arguments and see if they are accepted or accused of satire would be a good discriminator of something (I'm not sure what). What would it mean when an ideologies arguments can't be taken seriously unless you're sure the speaker is sincere?

You seem to leave out who the readers are supposed to be, and what kind of qualification about the ideology they would have to have. Ignoring that omission and assuming an arbitrarily "competent" reader, it would presumably mean that the ideology tends to be rather silly?

I know I can't charitably describe the arguments for the idea that discrimination against historically privileged groups is not a thing,

I think i also can't charitably describe arguments for that idea, as it hinges too much on something "historical". This is an inaccurate position to begin with, so the failure to argue well for it is not relevant. I mentioned some of this in an earlier comment. Quoting myself from there:

[...] i still believe that it would not pass, as i noted in my parens remark. This is because i think that none of "[institutional] power" or "prejudice" [against a group] can adequately be described as "historical disadvantage" alone. When they write "institutional power" as well as "power plus prejudice", they decidedly are not referring to something that lies purely in the past (indeed the present-day components are arguably the most important, though not the only interesting, ones) . The adjective "historical" in your usage seems to me to be incompatible to that.

This applies similarly to your wording regarding "historically privileged groups" (regardless that it is a variation on the "historical disadvantage").

I'd be interested what real feminists would say on the issue,

Well, it is said that there's one in my mind.

(and then whether that would be accepted by other feminists as representative of the ideology).

This is complicated by differing flavours of feminism, which i mentioned in your comment's parent (to handwave them away for the thought experiment).

I think that core statements i make about my feminism would usually be accepted "as representative of the ideology" (both feminism generally or my kind of feminism) by some people close to me, which happen to have similar ideological views. (How could that happen?!)

At the same time, it is plausible that lots of feminists would disagree. Hence claiming to be accepted "as representative of" the entirety of feminism might be very misleading then. Accepted by whom? Some majority of arbitrarily selected readers?

Anyway, when i initially wrote your comment's parent, i prepared my actual "submission" to the test already (but then decided to delay sending it). So here it is, adjusted:

[My] rationale for the 'one-sided' definition of sexism would be more along the lines of the mentioned "prejudice plus power", or "institutional power", or, say, "structures of kyriarchal (here incidentally also: patriarchal) domination which are frequently propagated by (plausibly subconscious) socio-cultural memetic effects which normalise/privilege particular traits".

I made up half of that last one, naturally. I consider this entire blurb relevant to the sexism definition because just "institutional power" seems too vague and hence could be misleading. The last one (my true one ?) traces more of the underlying ideology, or at least more explicitly.

Most feminists tend to be less verbose in a context like this.