Is it permissible to wash the private parts after performing ablution during a ritual bath, if the intention is to pray after completing the bath?

The Sunnah is for a Muslim to wash his private parts before performing ghusl (ritual bath), as it was narrated from Maymunah that the Prophet, peace and blessings be upon him, poured water on his hands and washed them, then poured with his right hand onto his left and washed his private parts, then followed that with the remaining steps of ghusl. If he touches his private parts after that, it is safer to perform ablution (wudu') after completing the ghusl, because touching the private parts invalidates ablution according to most scholars.