Lock them in the car. I walk in naked, towel(s), blanket, chairs, whatever is on call that day.I am very open about my nudity. When i hike etc, I do not carry shorts etc. I go naked. Its just who I am at this point.
Where can you do that? The few nude beaches that I have been to have clothing required signs between the beach and parking lot.
When I go to the beach I usually bring a chair or towel which I will leave my clothes with. I always have my phone due to my work and the long walk to get back to the car so I also leave this with the chair or towel.
Now for times where I go just to walk, I carry my shorts. I usually only wear shorts from the car to the beach because it is less to carry. I carry them because I am usually at San Onofre where I have to go onto Camp Pendleton (Marine base) where it is illegal to be on so if I see anyone coming, I can toss on my shorts and all they would do is tell me to go back north to the state beach side. I have talked to a couple of people where they got tickets from the MP for being nude.
When i go too the nude beach I usually carry my chair, a work out bag with cooler and snacks inside and a towel. Hopefully my surfboard if there are waves. I try to set up near other people so they might see someone with my stuff if I'm on a walk or out in the water. When strolling on the beach i always carry my phone and keys with me, usually in my hat. Haven't had any issues yet. I do bury my keys when in the water.
one thing i don't do with my clothes is worry about keeping them handy while at home. I used to have a pair of shorts stashed in the kitchen and upstairs in the den and would keep something handy while working in the backyard nude. But I gave that up years ago, if someone shows up and catches me nude , oh well, my home , my comfort.
We have not been to a nude beach but at Valley View HS. We leave our cloths in the car. I carry a back pack for my SLR and I put our valuables and keys in and lock the car. I have started carrying a tactical knife in the pack as well.
We usually leave them in the car! And sometimes we leave them at home when we are feeling daring! We have also left them in the meadow, along the trail, hanging on bushes. Sometimes it can be a bit of challenge to find them later though, More than once we had to drive home naked. Which is a different thrill than planning to drive naked.
My wife does not sea swim so if she is with me I have no problem as she will look after my clothes.
The only times I have gone to the beach alone have been on holiday and in that case I have always left all my clothing in the apartment or hotel room in the care of my wife.
Edited to add
I have a video of walking down for a swim here.
We have a backpack with our towels and sunscreen, so the shorts, t-shirt, and flip flops go in the backpack when the towels come out. Our car has a push to start ignition, so the "key" is just a small fob, which goes in the pocket of my hat along with a couple of $20s. Everything else stays in the trunk of the car. This system works for the beach and local camps. At Cypress Cove we get a wrist fob to unlock our room where everything but the towels and flip flops can stay. On nude cruises I wear my towel on the tender from the ship to the beach when we go to one of the private islands. Then I only need my ship to shore card and picture ID, which go in the same hat pocket. Plus, who would steal our stuff when everyone on the beach is from the same ship?
The last time we were on Orient Beach we took a taxi from our cruise ship so we could see first hand the destruction from hurricane Irma. That day we had more clothes plus our wallets, so we picked two beach chairs near the guy renting them so somebody would be watching our stuff while we were walking around. Threw our clothes in the backpack and then threw our towels over the backpack when we left the chairs. In the past we would have rooms at Club Orient, so wallets and clothes would stay in our Mini Suite and we would charge everything to our room, so a key (with a coil wristband) and a towel would be all we would have out on the beach.