If the problem only manifests itself when you plug in the charger for the phone, it’s not a ground loop problem. Is this a charger from a reputable manufacturer or some cheap unit? It sounds like they omitted any type of line filtering and the high frequency switcher is back flushing into the car’s electrical system or radiating a heck of a lot of noise.
Naturally, grounding of both the new radio and the antenna feeding it is important. This allows the radio’s internal filtering to bypass any noise conducted on the power supply input lines into the chassis ground. Likewise, an ungrounded antenna will pick up the slightest radiated noise and feed that right into the radio.
Personally, if I new the grounding was correct, I’d try a different charger first.
Barring that, you could install a line choke filter on the power supply for the radio to augment its own filtering. This common mode filter will block any conducted, high frequency noise from entering the radio power supply. They used to be more commonly used years ago but most electronics now has to meet Class A or B emissions and be tested to not interfere with other electronics (i.e. EMC standards). Most stores that sell radios will have these line chokes near the installation parts. Crutchfield also sells them…