Why is a solution of PCl3 more acidic than MgCl2?
There is no such thing as a water solution of $\ce{PCl3}$. It reacts with water, and quite vigorously. Once the reaction is over, there is no more $\ce{PCl3}$ in the solution. Arguably, there is no $\ce{MgCl2}$ in the other solution either, but it would form (as a hexahydrate) if you evaporate the solution; $\ce{PCl3}$ would not.

The reason for this is that $\ce{Mg}$ is a metal and $\ce{P}$ is a nonmetal. They are different elements, about as different as two elements can be. They have nothing in common, except for a few sparse random traits, like being able to burn brightly in air when ignited. No wonder they are different in this regard as well. $\ce{MgCl2}$ hydrolyzes only very slightly (say, one part in a million). $\ce{PCl3}$ hydrolyzes completely.