Is the Hadith that the Prophet (peace be upon him) urinated standing up authentic, and how do we respond to those who deny its authenticity?

The hadith is authentic, narrated by Al-Bukhari and others. If a hadith is authentic, there is no alternative for a Muslim but to follow it. The imams of Islam acted upon it and did not interpret it allegorically. This is something the Messenger brought, and therefore, it is obligatory to submit and yield to it.