How do I reassure myself that I am a worthy candidate for a tenure-track position, when department would likely have interviewed me even if I wasn't?
There are two things worth keeping in mind. First, while it might be the case that the committee is "forced" to interview a female candidate, it might not. You have no actual evidence in either case, and though it's tempting to assume the worst, there's no reason to, and there's absolutely nothing to gain by thinking the search committee doesn't want you there. So: spend your mental energy working on your talk, your research plans, etc.

Second, even if it is the case that the committee wouldn't be interviewing you if left to itself, the interview is in many respects a "blank slate" -- an opportunity for candidates to impress potential colleagues beyond what's evident on paper, and (of course) for candidates to fall flat and perform terribly. I've been on enough search committees to assure you that several of your fellow interviewees will do terribly, and that conversely it is not uncommon for committee members to say "I wasn't really in favor of bringing X to campus, but now having interacted with him/her, I'm glad we did."

This is all, I suppose, a long-winded way of saying "worry less, and always do your best!"