Having just returned from glorious week on the island, here are my observations regarding Nudist beaches:
El Cotillo. La Concha beach (looking to the right from Bar Torino) is pretty much textile now. I certainly wouldn't be comfortable stripping off, especially given the reaction of some families with kids. The next beach after La Concha (past the two oddly shaped houses - location
28.696054, -14.016557 on google maps) is usually nudist but can be fairly crowded and not great for swimming, except at high tide.
I was able to take an early morning nude swim every morning right outside our apartments (Cotillo Lagos location
28.690132, -14.011933 on google maps) closer to the town. So long as I was out and dressed before 9.30am when the beach suddenly fills up! I was also able to sunbathe nude in one of the many cairns on this beach.
Corralejo Dunes: The beach in front of Reynaldos (Playa El Bajo Negro on google maps) was fairly relaxed, though myself and the wife were probably one of only two heterosexual couples there! I did notice a fair amount of what looked to me like 'cruising' activity - I went for a walk toward flag beach to see if there were any more suitable swimming locations and random guys would pop up out of the cairns like meerkats

I'm in no way bothered about this, but I'll be directing my gay friends to this beach in future
Mal Nombre: We took a drive south to investigate the beaches there and I have to say I agree with Magoo. Playa Del Mal Nombre near the beach restaurant Tierra Dorada was one of the most relaxed beaches we've ever been on. There's a mixture of clothed and naturist folk there but an atmosphere without the edge you'll find on mixed beaches at El Cotillo. Spent a wonderful day there, swimming conditions were excellent, and the restaurant was pretty good too!