This is called “fish eyes” and typically comes from silicone oil contamination. The usual culprit is Pledge furniture polish. No amount of stripping is going to get rid of it. It will affect varnish, lacquer, and water-borne finishes the same way.
The best cure is to strip off the fish eyed finish, once again. Sand. Re-stain, if desired. Then apply two coats of DEWAXED shellac. A good choice for this is Zinsser’s Seal Coaat.
Poly will have problems adhering to waxed shellac.