This essay argues that the current Roman Catholic ecclesial climate with respect to its teachings on gender identity and sexual orientation constitutes our own contemporary version of the Galileo Affair. After a consideration of the historical circumstances of the Galileo Affair of the 17th century, I argue not only that the institutional risk factors for a subsequent Galileo Affair have not been adequately mitigated; I argue also that the presence of discourse impasse, preemptive judgments, and exclusionary policies on the part of Church leaders make it likely that we are in the midst of another Galileo Affair.