I wanted to follow up with an update on this. We were in Dubrovnik on All Saints' Day, and we did not experience any interference with our plans. That morning, we visited a Serbian Orthodox church for the worship service, bought a quick borek for lunch on the street, visited the local cemetery (there was a special All Saints service that we were curious about), and then headed out to walk the walls (amazing). That evening, we walked through the town, shopped, and had dinner out. Though it was a holiday, catandmouse was exactly correct that business remained open for us tourists.