In the movie we see Professor X wearing three suits. On the day in question, he wears a dark blue suit with matching trousers.
Under the circumstances, we can presume from the fact that he also supplied his own non-metallic wheelchair (knowing that he'll need to pass through a metal detector) that the Professor personally owns at least one pair of suit trousers, either with a nylon zipper or plastic buttons (hat tip to @benBolker for pointing out the obvious).
It would be highly unlikely that the prison would supply clothing to him, let alone a stylish custom-made suit.
On the wider issue of whether the plastic prison supplies clothes to people who inadvertently wear metal, my guess is that they follow US prison visiting procedures and bar entry to those who can't follow the rules:
"The dress code will be strictly enforced. It will be the inmate’s
responsibility to communicate these standards to his/her visitors"