What about a variation like this one where yiu have to stick it in the hole first and then slide it down? That means it can still lift up,but because it isn’t totally open on the other side, it offers up a little protection from popping out as easily.
Also don’t discount the idea of altering your original bracket or the one I linked to. Adding a piece of wood (or 3D printed piece) that pivots out if the way would mean removing the fan is a 2 step process. You swing that wood piece up first, amd then slide the fan up. Still super easy to move, but less likely for it to happen accidentally.
Or add a cotter pin that slides into a hole that then blocks the opening to prevent accidental removal. A short chain on the cotter pin keeps it from getting lost. In industrial environments, cotter pins are used all the time for that purpose.