Newtonian “zero net pull force” at center of star/planet vs. GR singularity of black hole

Question

1. At the center of a black hole, tidal forces become extremely large (classically infinite at the singularity).

2. But in a Newtonian model, the net pull at the center of a spherically symmetric mass distribution is zero, cf. e.g. this and this Phys.SE posts.

How do I reconcile these statements?”