When reading about the history of Ethiopia, it's often mentioned how contact with the rest of the Christian world was more or less lost after the Muslim conquests. Considering that there are lots places in the Mediterranean mentioned in the New Testament (like Jerusalem, Rome, Antioch etc), was there any interest in visiting these or establishing contact with religious authorities there?
So, a couple things. Yes, Ethiopia was fairly isolated, especially when the Muslim states that surrounded them took away their access to the sea. But they were still connected to the rest of the Christian world through Egypt, and there was regular exchange there, in the form of Egyptian bishops coming to take the overlordship of the Ethiopian church (which would not see Ethiopians appointed to this position until the 20th century) and through Ethiopian monastics traveling through the various Egyptian monasteries on their way to Jerusalem. This, however, was a one-way trip, and the intention was generally to die in Jerusalem, but there is a long-established Ethiopian community in Jerusalem for just this reason (in the 20th century, Egyptian monasteries started making their living conditions more comfortable and as a result, the Pachomian Ethiopian monks, committed to a life of poverty with no frills, stopped going to the Egyptian monasteries, and, alongside easier travel, started going directly to Jerusalem).
Another avenue where Ethiopians expressed interest in the wider world, and Egypt in particular, was through the acquisition of artisans to work on major church buildings. It is thought that several phases of Egyptian artists were recruited to help embellish the interiors of churches like Yemrehana Krestos, and that Ethiopian artists learned and incorporated Coptic art styles, part of a normal pattern of exchange of art that occurred throughout the Christian Mediterranean. Judith McKenzie has argued (persuasively, in my opinion) that the Gospels of Enda Abba Garima, the oldest illuminated four gospels manuscript in the world, is a native production of Ethiopian artists despite earlier claims that it was imported due to elements of Syriac style in it. As part of that argument, she lays out not only specifically-Ethiopian elements of the illuminations, but also the extent to which the Christian Mediterranean, Ethiopia included, shares artistic motifs across space and time.
More recently, Verena Krebs has recently written an excellent book (first chapter available here) about Ethiopian interest in the wider Christian world in the 15th century, where she overturns earlier narratives about Ethiopian-European contact by establishing that much of the contact was driven by Ethiopian monarchs who were primarily interested in religious arts, artifacts, and craftsmen for religious foundations. Europeans, on the other hand, mostly hoped that their legend of a powerful Christian king in Ethiopia were true, as they looked for allies against the Ottomans. Finding a kingdom restricted to the highlands that did not really compare to European powers in terms of military might meant that they largely (but not entirely) lost interest in Ethiopia until the colonial period.