The University of Oxford was founded in 1096 as a Catholic university with a curriculum in theology and canon law. The University of Cambridge was founded in 1209 by people from the University of Oxford, so also largely clergy. The University of Salamanca was founded in Spain in 1218, also to teach theology and canon law (and, in fairness, some harder sciences as well). The first subjects to be taught at the University of Padua when it was founded in 1222 were law (civil law and canon law) and theology.
And while it's true that the University of al-Qarawiyyin was founded as a mosque, mosques in that time were well-known and attested as places of learning; there's evidence that al-Qarawiyyin was a madrasa from the very beginning (and proof of it by the 12th Century at the latest), and while people in European universities try to draw a distinction between the definition of "university" and "madrasa," there's no real evidence for a meaningful difference that doesn't just boil down to "well, they do stuff differently."