No, Croatia is not "very socially conservative". It is maybe a bit more conservative than typical EU state which is still way more progressive than American notion of "conservative" let alone "very conservative".
Then the thing is that places mentioned in the thread are not conservative at all. Coastal towns are not conservative.
I come from Split and I have never ever had any troubles or whatsoever of being shirtless. You know that we only have those fines because of uncultured tourists. Because they think they can enter museum or bank in their swimsuits.
Also there have always been undesignated nudist zones everywhere. There's one 20 minutes walk from Split downtown. On the islands, wherever urbanization stops, there could be naked people on the rocks of the shoreline. They just move a bit away, like 200-300m further from the last accessible beach in the area, and sun on the rocks. Every child that has spent more than 2-3 hours in a boat in Dalmatia was bound to see naked human genitalia up front or in the distance.