Yes it is safe to store food in plastic containers.
Most if not all plastic containers made and sold today contain no BPA or other bad chemicals in them that could leach into the food.
I use plastic containers to store food in and have done so for years and so has my grandma and my mom and we never have gotten sick from any of the plastic containers and even when the plastic containers contained BPA.
I mostly use food storage containers that are made of plastic but I also store food sometimes in plastic butter containers, whip cream containers etc.
Never had any issues storing food in any of those plastic containers either.