Not all Motorola’s can be republic wireless compatible phones but luckily, The Moto G devices can work with Republic wireless. There are a wide range of the Moto G phones and they vary from Generation from generation.
Republic wireless relies on Sprint to provide network coverage. Both Sprint and Verizon use the same network technology which is CDMA and LTE. Most of the Motorola G phones can work under LTE hence they can be compatible with Verizon and also Republic wireless.
However you should check with Republic wireless to ensure that they offer their services in your area so that you do not suffer from low network signals.