Supermarket HDPE plastic bags safety
Polyethylene is generally considered suitable for food handling and even for warming food. Unlike some plastics such as polycarbonate, it does not need an additional plasticizer that could be toxic.

That said, the melting point of polyethylene is ~1150C, and I've found that it tends to shrink-wrap around microwaved food. For that reason, polypropylene, m.p. ~1300C, is often used for food containers intended for microwave oven use and for automatic dish-washing.

BTW, both polyethylene and polypropylene absorb some of the natural lycopene coloring of tomatoes or other carotenoid pigments and slowly develop a pale brown discoloration that cannot be removed, but that is of no significance.