I avoid or minimize tear out by "sneaking up" on the final turned surface. Often, heavy turning removal can disrupt the grain below the surface and leave quite deep tear out. Try taking several very light passes with a sharp scraper. I keep a bull nosed "negative rake" scraper just for this purpose. It takes very light cuts - cutting all the way. You should then be able to start with 150 grit paper.
When sanding out the inevitable minor tear out, try applying a finish (I use shellac), then sanding. It seems to stiffen the structure which sands more easily. Also if your lathe will reverse, sand in the opposite direction. Even if you don't see the effects of tear out on the sanded surface, it will become apparent when finishing - it will appear a lighter colored areas. I think of these as "bruised" areas. This is mimnimized with the negative rake scraper approach. You can search the web and find descriptions of how to turn any scraper into a negative rake scraper.
Don't give up on walnut - it is a great wood!
Jerry