Should I disclose gender, race, disabilities etc. in tenure track job applications?

I guess if I were Male, Caucasian, non-disabled etc I might lose an edge due to preference towards minority candidates; while if I were Female, Black, disabled etc I could gain an edge?

There are limits to how protected characteristics can be used in affirmative/positive action. By authorizing them to use this information, you can benefit from permitted affirmative/positive action if you qualify. If you do not authorize the use of the information, then you cannot benefit. In regards to permitted affirmative/positive action there is no benefit to withholding information.

There is also a possibility that this information would be used for un-permitted/illegal discrimination. In general, however, illegal affirmative action where minorities are given an advantage does not happen. Rather, there are all sorts of documented implicit and explicit biases that help white male applicants.

In my opinion, if you are not a minority (e.g., a heterosexual white christian male), there is no risk in making the information available. If you are a minority the choice is more difficult. You could benefit from affirmative/positive action, but you could also open yourself up to implicit and explicit biases.

Quite frankly, I would suggest to fill in the data and be done with it. I assume you are male, and I guess if there was something "interesting" to tell about you, you would have done so.

I assume that the final decision will not be based on that form alone, either, but will be found after they got to see/talk to you in person. Hence, everything you can fill in will then, finally, be revealed anyways.

If "gaming the system" is of interest to you, look no further than statistical data about the place you are applying to. Are there a high percentage of women/black/disabled people there? Do you clash against the description? Then you may want leave the data off. But you never know how they discriminate (speaking neutrally). The fact whether the data is hidden may even influence them, if not officially, then at least subliminally. Same with every other fact.

In general, I would assume - from a pure psychological viewpoint, and some first-hand experience - that very few to zero deciders are truly and utterly free of prejudices or bias with regards to at least some aspects on that form. Your problem lies in the fact that you cannot know where the bias lies, again assuming that you do not know the people who will read your resume/form. I'm not talking about obvious things like "we cannot decide based on skin colour" or "we need one more disabled to fulfill our quota", but deep-rooted opinions, maybe unconscious ones.