Yep, almost always have a crossbody purse. Sunscreen is a necessity for me, as is a hat and sunglasses which I stuff in there when on rides or inside. Refillable water bottle, phone and charger, poncho, tissues, ID, credit card, ibuprofen, some cash, reading glasses in a case. I have a medication which should be taken around 3 PM so that also. I don't carry a purse at home, but do have one in the parks.
Occasionally if I am onsite at Universal and go back to the parks in the evening I can skip a lot of that and use pockets, since the resorts are so close to the parks.