Well the empirical evidence is that probability and stochastic processes are going on all over the universe,at all levels, in living and nonliving matter and in energy, and have been for billions of years. Whether one wants to call these "accidents" or not isn't really a scientific issue. But they are clearly happening.
It appears Einstein was wrong, not only does God play dice, but he has Avogadro's number of casinos per mole of substance.
Can Christian theology be reconciled with this fact ? I've always thought so. But at least in the US, anti-evolutionism seems even to be creeping into Catholicism of late. Maybe the (next?) Pope needs to crack down on this ?