According to Javier Matallanas of Diario AS (h/t Sport), Ronaldo made the demand as he is "fed up of the Los Blancos medical services" and "doesn't want certain situations from last season to repeat themselves."
He is reportedly not the only one at the club unhappy with the club's medical staff as the players collectively do not want the doctor who heads the team, Dr. Olmo, though Perez will not be relieving him of his duties as he has "stood firm in his decision to not change the current medical team."
Sport has previously reported (per Jack Ling in the Sun) on Ronaldo's frustration with the medical staff at the Santiago Bernabeu, with the newspaper noting in April he had even turned to Barcelona's physios as he looked to recover from a hamstring injury after Real's staff neglected to give him a scan.
There were even suggestions that Ronaldo's anonymous performance in the UEFA Champions League final in May was caused due to a lack of fitness, though Madrid boss Zinedine Zidane refuted the claims, per football writer Miguel Delaney:
Not every player seems to be unhappy with the physios at the Bernabeu, however, per the Times' Gary Jacob (h/t ESPN FC's Dermot Corrigan):
Bale spent a fairly significant portion of last season out injured, restricting him to just 23 La Liga appearances, though he seems not to attribute his absence to any failing on the physios' part.
Nevertheless, Ronaldo is now 31—managing his fitness will become even more crucial as he gets older if he's to prolong his career and keep himself playing at an elite level in the years to come, so his concerns are understandable.
Equally, it's in Real's interest to keep him fit and firing on all cylinders, so the decision may prove to be a shrewd one even if it's not to the liking of the other physios working at the club as Matallanas suggests.