Do these rules make it illegal for hobbyists to fly drones in areas without internet access?
Drones with "limited" remote ID capability would not be authorized to take off without internet (because they have no radio broadcast), and if they lose connectivity in flight they are supposed to land.
Note that this is for ALL unmanned aircraft not just drones.
Limited Remote Identification will be the cheaper type and can not take off without an internet connection.
Standard Remote Identification will have equipment to radio broadcast location data and can take off without internet connection.
See table on page 98
https://s3.amazonaws.com/public-inspection.federalregister.g...
Your other options are to fly < 0.55lbs or fly in specially designated areas, like model aircraft club airfields.