Can life survive on the equator of cooled and fast rotating white dwarf or neutron star?
I am going to attempt a weak answer, mods feel free to delete it, but I'm fairly certain I'm right.

Shortly - no. It's not possible. Even if you balance gravity and centrifugal force perfectly at ground level at the equator, they will very, very quickly become imbalanced as soon as you move north, south, or up from there. So quickly in fact that the gradients may be too big even for a human being not moving at all. Maybe if you're laying down, with your body oriented along the equator, but even then I think the gradients would be too big.

Maybe bacteria would survive, briefly.

I'm sure the math could be done quite easily to estimate the gradients. This is based entirely on intuition.