The debate over intuitions is one of the hottest in philosophy today

But it -- at least the "debate over intuitions" that I'm most familiar with -- isn't about whether intuitions are reliable, but rather over whether the critics have accurately specified the role they play in traditional philosophical methodology. That is, the standard response to experimentalist critics (at least, in my corner of philosophy) is not to argue that intuitions are "reliable evidence", but rather to deny that we are using them as evidence at all. On this view, what we appeal to as evidence is not the psychological fact of my having an intuition, but rather the propositional content being judged.

The purpose of thought experiments, on this view, is to enable one to grasp new evidence (namely, the proposition in question) that they hadn't considered before. Of course, this isn't a "neutral" methodology because only those who intuit the true proposition thereby gain genuine evidence. But the foolishness of such a "neutrality" constraint (and the associated "psychological" view of evidence) is one of the major lessons of contemporary epistemology (see, esp., Williamson).