It is the custom in the United States for most restaurants to be open on Sundays. (Chick-fil-a would be a notable exception.) If you eat, somebody’s got to do the work of preparing the food, whether it’s you or someone at a restaurant. Eating at a restaurant actually helps the family to keep the Lord’s Day holy, by freeing them from having to cook.
Orthodox Jews prepare all of their food beforehands, so as not to have to cook or prepare food on Shabbos. They even use ways to keep food warm, placing it in or on heating units that have been turned on prior to Shabbos, so as not to have to “light a fire” which is forbidden on Shabbos. I have also noticed that some evangelical Christians do their cooking on Saturday night, apparently to free themselves up for a day of worship on Sunday, and to make food preparation on Sundays minimal.