The anthropic principle doesn't need it to be typically stable though, right? It could be exceptionally stable, in a particularly evil universe, and we'd most likely crop up in a nice little stable oasis.
If it were unstable during the 4 billion year history of life it could wipe life out and we wouldn't be here to observe it. But it depends on the magnitude of "unstable".
Our sun is exceptionally stable - it has no close encounters with other stars that might disrupt planetary orbits, which does happen in galactic nuclei or globular clusters. We are in that nice little stable oasis.