Keep the strength requirement, but there should be no repercussions other than identity for breaking people's HFs that just happen to be laying around unsecured. Also make their shit dump all over the ground. A logged in active HF might still preclude vandalism and the having of criminal skills so people can't fuck with you too cheaply while you're out and about actively gathering resources as long as you remember to rehearth in a secure location before you log out.
Incidentally, this would go nicely with mak\ing HF's accessible inventories containing equipment and inventory and an HFless char should dump their shit where they log out and have to log back in naked and pick their shit up if they can.