Nationality, ethnicity, and ethnoreligious identity can co-exist, and are not mutually exclusive. Particularly where you are dealing with ethnic and ethnoreligious identities with millennia of development, the idea that you cannot be a Persian Jew simply doesn't align with history.
With that said, to be Middle Eastern is no different than saying you are British, so it's an area designator, not a clear ethnic identity. So by saying her Dad is Middle Eastern, that's not to say he's Persian. We know he's Sephardi, so presumably at some point his family were in the Iberian peninsula.
Simply put, both her parents are Middle Eastern, and both her parents are Jewish. Given that Judaism is an ethnoreligious group originally from the Middle East, that's not as unusual an identity as you may imagine. Remember, "Middle Eastern" is not an ethnic monolith, but a wide number of people groups, many of whom have been interacting (both peacefully and with significant conflict) for millennia.
