Is it rational to trust your gut feelings?

It depends, of course. Ideally rationality works with feelings to make the best decisions. Too much in either direction can lead us astray. Unbalanced rationality can lead to ad-hoc rationalizations or justifications. Unbalanced feelings can lead to us to overindulge or maintain in-group biases. Balancing them is dynamic, with one side weighing more or less heavily depending on contextual factors.

But interestingly, these two systems are distinct and uncorrelated, each operating on their own. So while we can balance them they are not part of the same processing continuum. I.e., thinking doesn't transcend and subsume feeling in a nested hierarchy. They are more like the structural coupling of systems science discussed here where I said:

Different domains in a human being are different systems that have to communicate with each other via structural coupling.

"In Luhmann's theory the 'human being' is not conceptualised as forming a systemic unity. Instead it has to be understood as a conglomerate of organic and psychic systems. The former consists of biochemical elements, the latter of thoughts. Both systems are operatively closed against each other: no system can contribute elements to the respectively other system. The systems are however structurally coupled; i.e. their respective structures are adjusted to each other in such a way as to allow mutual irritations" (9-10).

Only with integral-aperspectival awareness do we 'integrate' the various levels-systems, not by subsuming them into the higher or unitary level but by the levels now structurally coupling with and communicating with each other. Our consciousness is now an hier(an)archical multiplicity with many often irritating voices.