Answering myself: the beach next to the Red Mountain is ok, plenty of happy naked people, nice natural beach, a bit of rocks next to the mountain to explore. Approximate coordinates: 2CJX+35G (28°01'48.0"N 16°33'07.0"W). A lot of good accommodation around Street Market La Tejita, west of the beach. Probably close enough to stay in El Médano too, but I didn't test that. Chiringuito Pirata El Médano is a nice bar too, very friendly staff and excellent service, happy vibes. I'll definitely be back, probably as soon as the next April. I was there alone, so not ideal (I really hope I didn't stare too much, I tried), but I'll be back with friends. There's a few textiles walking around, and I think someone took a picture of me, but it's an open area, so I guess this is not easily avoidable. Sometimes strong winds, but it's still good, the rocks and stones keep the blankets in place. Please remember to use the sun block!

1. I wouldn't, I'm shy, I like to spend time naked in nature and when there's similar open minded people around, but I don't feel comfortable being naked next to people who aren't friendly or understanding.
2. Not much. Certainly I wouldn't try to convince anyone to do it. It's not for everyone and it's ok. But I also think humanity, in more general sense, could use a bit more of understanding and forgiveness. Just live and let live. If you don't like it, don't do it, but don't criticize or punish others for things you don't understand.

I'm thinking about flying to Canary Islands a couple of weekends, when my local lake gets too cold.