I nice way to explain this would be to realize that questions asked about a lie detection machines use would ask about its accuracy. The only pair that says this is legitimacy and validity.

The other pair, feasibility and practicability, are applicable to machines and technology but are not as relevant as legitimacy and validity.

Why not feasibility and practicability? I think it fits well with inclusion.

Although many proponents of lie detection desire to engage disciplines outside of law enforcement and to stimulate interest in the progressive success of science's newest machine. This sentence suggests a contrast between the two sentences.
Now the clue for the blank is right there in the sentence itself.
If we look at the part of the sentence: the history of mechanical lie detection are fraught with questions of ___________ and inclusion., there are two problems indicated. One is the inclusion and the other is the blank.
inclusion points to the part of the sentence: desire to engage disciplines outside of law enforcement. So the blank should correspond to the other idea presented in the first sentence: to stimulate interest in the progressive success of science's newest machine. Success of the newest machine, so earlier the questions were about the success of the machine, it's validity and it's legitimacy.

Thank you for breaking sentences. It helps me a lot.

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