I don’t see how this order has any teeth, landlords should simply continue evictions. We already know it is unconstitutional, and, except for Kavanaugh deciding public policy rather than law, would have been struck down, and will be again.
In most states, (especially blue states), the local courts will not even allow “unlawful detainer/eviction), cases to be filed or if filed they will not assign a court date. Landlords need to file federal court suits against the CDC. In their state they may need to file a suit asking the state supreme court to order the lower courts to allow the eviction cases to go forward.