As pretty a cedar can be, it's still a soft wood which makes for difficult turning to a smooth surface. You are going to be going directly against the grain at some points. It will take a ton of sanding to get out 1/8" deep blow outs, way more than you want to do. The same basic thing can happen when doing cabinet work with figured grain. Some of the tactics used in that work may be applicable for you.
The cutting bevel used on plane blades and machine knives is changed to a more blunt angle. You didn't say what type of turning tools you are using. Perhaps a change in the angle could help. Scrapers can also be a way to go. As always, the key is seriously sharp tools, very light cuts. Wetting the surface of the work can help, makes it a bit more pliable rather than brittle.
What are you using for a finish? Probably not the Bush! If something like linseed oil, mineral oil, you could try heating it up, double boiler, no open flames, preferably outside and applying as much as you can soak in while you still have about 1/8" yet to go on the turning. In the olden days, we did shaker tables in pine, kept slathering the top with warm linseed oil until it bled out the back side, so I know that will penetrate.
If you can determine where the grain is likely to give you problems, you may be able to coat that area with Crazy glue. The big issue is avoiding the blow out rather than trying to remove it. Those sanding tools by Robert Sorby work very well but are not that great up against a ridge and other precise areas. They give a random orbit like cut so you don't have straight striations like you do holding sandpaper. Excellent for smooth surfaces.