Such garbage and rubbish collection and disposal services may be financed in whole or in part by a levy of a tax on all property in the county only if all persons in the county are to be equally served, but such a county-wide levy shall be unlawful if any city, town or special district in any city or town, that, through its own forces or by contract, provides such services within its boundaries, or if any other part of the county is to be excluded from the service area.