You say part-time. Do you mean temporary by any chance?
If a company decides to lay off temporary workers, they would be entitled to set that as a criterion.
Assuming you do mean part-time, there is no clear answer. The employer must publish their criteria for selecting people for redundancy. If they have chosen to operate with only full-time staff for good operational reasons, that would probably be fair selection for redundancy. It is easier to run a company with 20 full-time employees than 40 part-time employees.
The company should consult with employees and the employees could make a case why they should not be made redundant. It would certainly be acceptable for an employer to make performance a criterion for selection for redundancy. In my view, that would be a more sensible criterion than whether or not their work is full time or part time.
Brendan