First of all, that’s not yet completely clear - we hardly have a complete accounting of all biological processes. But it is true that the processes we have accounted for so far are classical.

Second of all, quantum non-determinism still influences classical processes, especially chaotic ones where small shifts in initial conditions have a great effect on the long term outcome. See e.g. the weather, which is an entirely classical phenomenon, but where quantum fluctuations create a floor for how far into the future you can predict the weather even with perfect information and infinite computing power.

So quantum non-determinism allows for classical non-determinism.