No, Ralliart and Prodrive were not factory teams. But they were 'manufactuer' teams.
M-Sport get technical support - a grey area to what that amounts to - but not enough funds from Ford to officially call it a Manufacturer entry.
Citroen and Hyundai are factory teams. Their motorsport divisions are owned by the car manufacturer. Toyota is a manufacturer team with the car manufactuer outsourcing and funding the programme.