Elaine Roberts, a longtime bagger at a supermarket, tried to be so careful. She put on gloves and stopped riding the bus to work, instead relying on her father to drive her to keep their family safe. She wore masks — in space-themed fabrics stitched by her sister — as she stacked products on shelves, helped people to their cars and retrieved carts from the parking lot.

But many of the customers at the Randalls store in a Houston suburb did not wear them, she noticed, even as coronavirus cases in the state began rising in early June. Gov. Greg Abbott, who had pushed to reopen businesses in Texas, was refusing to make masks mandatory and for weeks had blocked local officials from enforcing any mask requirements. The grocery store only posted signs asking shoppers to wear them.

Ms. Roberts, 35, who has autism and lives with her parents, got sick first, sneezing and coughing. Then her father, Paul, and mother, Sheryl, who had been so cautious after the pandemic struck that their rare ventures out were mostly for bird-watching in a nearly empty park, were hospitalized with breathing problems.