I was on Kemil every day from 9/23 through 9/30. Each day was a combination of nude and severely minimal swimwear. Most of the time, I limited the nudity to back in the grass, but there were several times I gut nude down on the beach. I went skinny dipping from a deserted beach with no one within 1/3 of a mile either way, but with a boat anchored off shore directly in front of me.
As long as I had some type of minimal swimwear on, I felt comfortable laying out directly on the beach. I wore everything from a G-string with a sheer pouch, to several different thongs, sheer bikinis, and sheer shorts. I walked the beach and trails in a thong multiple times.
Throughout the 7 days on the beach, I had no issues.
That area of Kemil Beach during the summer will be far too busy to get naked. You had an awesome late-season experience, but normally there are going to be crowds of people in that area, unless I'm thinking of the wrong space. If you're able to find someplace out there to get naked other than the State Park beach during the summer, please let us know!