There's 2 sides to this.
Evaporation takes place inside the evaporator and makes the coils cold. Room air passes over the evaporator coils and the heat from the room air gets transferred into the cold coils. At a practical level, the evaporator coils can frost-up and thus reduce the efficiency of the transfer process. Humid air is also less dense than dry air so, even if the evaporator does not frost-up, the evaporation process is not as efficient and less cold will get transferred to the room air.
The condenser coils transfer the heat from the refrigerant to the outdoor (atmospheric) environment. Some condenser coils (for example in boat/marine applications) are designed to be submerged in rapidly flowing water to carry away the heat. Automotive condenser coils need to work when they are wet or dry. They rely mainly on air flow (fans or forward speed of the vehicle). Efficiency of the condenser coils can vary depending on the amount of airflow, the temperature gradients between outside air and coil temperature and corresponding dew-points. If there is adequate airflow over the condenser, humid outside air or rainy conditions can improve efficiency. If the dew points are high and there's not much air circulation, condenser transfer efficiency decreases.
There's no easy answer to this because thermodynamic theory gets clouded by reality. In the absence of sufficient air flow, high outdoor humidity decreases the efficiency of the condenser coil transfer process. In some less common cases, high humidity and airflow can help the condenser process. Finally, high room humidity can decrease the efficiency of the evaporator coil transfer process.
(In a nutshell, humidity is evil in most circumstances).
Ray