Assuming we are talking about America.
I think urgent care is a toss up. In fact I would bet most aren’t open.
Police and fire and hospitals are all open.
Hotels, Disney World, most movie theatres, gas stations and many Chinese restaurants—open. Many restaurants are open Thanksgiving with special menus that include turkey, but most are closed on Christmas unless it is in a very tourist driven area. Tourist areas have much much more open than your average town. But, the Chinese restaurants are a tradition for being open on Christmas day, but still no guarantee.
It used to be all retail was closed Thanksgiving and Christmas, with the exception of some 24 hour stores and some food stores sometimes were open Thanksgiving morning. Now, some retailers will be open Thanksgiving. Christmas day seems to still be sacred though. You can shop Christmas Eve day though. Most mall stores are open until 6:00 pm Christmas Eve.