Split is a city and the only beaches there around are textile. I would recommend a few hours or an overnight stopover to take a look at Diocletian's Palace but if naturism is a priority, then you will have to move somewhere else. Your options on the coast include Nugal beach at Makarska, cannot personally comment as have not been there or on that bit of coast. Makarska is modern as Croatian towns go due to being in the earthquake zone and probably not all that interesting. If you search my and Jonny's posts here we have written in depth on Hvar, Korcula, Mljet and Vis, and any two of those islands would be a absolutely superb holiday. Beaches are not 'official' strictly speaking but recognised...you might find in July and August in Hvar on the Pakleni islands getting crowded by beachwear fans though.

Much appreciated Briggitte, I'll take a look at your suggestions.