This was an issue for me when I first started studying “analytic philosophy” which came out of the “linguistic turn”. While some traditional Catholics consider analytic philosophy to be a lot of sophistry and hair-splitting I think it’s really great. In fact, I consider it to be the modern version of scholasticism. Like the scholastics, the analytics use precise language, specialized terminology, logical rigour, and clear argumentative form.
While many of the early people, like Russell, Wittgenstein, Carnap, Ayer, Quine were all radical empiricists and materialists, so far analytic philosophy has come to include many famous theists and even Catholics. As you say, the Church’s philosophy traditionally (though not exclusively) relied upon a broadly Aristotelian conception. This has been defended by such eminent thinkers as Kit Fine, E.J. Lowe and Michael Loux. In recent years Catholic + Christian philosophers have brought the traditional philosophy and theology of the Church to bear in contemporary analytic philosophy, creating what’s called “
analytic Thomism”.