Even as various states shut down different types of businesses and ask people to shelter in place, the U.S. Department of Homeland Security designates the Food and Agriculture industries as critical infrastructure.
Presidential Policy Directive 21 (PPD-21) classifies agriculture as one of sixteen critical infrastructure sectors, "considered so vital to the United States that their incapacitation or destruction would have a debilitating effect on security, national economic security, national public health or safety, or any combination thereof."
Read about it on the U.S. Government website
Therefore, know that the government will not force the shutdown of stores, either brick-and-mortar or online, that provide supplies and feed for your animals.