Bukhari

Hadith Commentary:
In this narration, "Hujjat al-Haruriyyah" refers to the military campaign of the rebellious armies of the Ummah against Abdullah ibn al-Zubayr (radi Allahu anhu). This event took place in the year 73 AH. Although Hajjaj himself was not a Kharijite (Khariji), like the Kharijites, despite his claim to Islam, he violated both the sanctity of the Sacred Precinct (Haram) and of Islam.
Therefore, the narrator likened his attack to that of the Kharijites and, in a sense, considered it an assault similar to that of the Kharijites, since he launched an offensive against the rightful Imam, i.e., Abdullah ibn al-Zubayr (radi Allahu anhu).
By saying "Hujjat al-Haruriyyah," the intention is to allude to the vilification and the Kharijite-like action.
The Kharijites performed Hajj in 64 AH; it is possible that Abdullah ibn Umar (radi Allahu anhu) performed Hajj in both of these years.
The correspondence between the chapter and the hadith is as follows: Abdullah ibn Umar (radi Allahu anhu) purchased a sacrificial animal on the way and combined Hajj with ‘Umrah, and he said that if he were prevented from performing Hajj, then the Messenger of Allah (sallallahu alayhi wa sallam) was also prevented by the polytheists from performing Hajj in the year of Hudaybiyyah, and he (sallallahu alayhi wa sallam) released himself from the state of ihram at that very place and had the sacrificial animals slaughtered. He (Ibn Umar) said, "I will do the same." However, this did not happen to Abdullah ibn Umar (radi Allahu anhu); rather, he was able to perform all the rites of Hajj at their proper time.

Hadith Commentary:
(1)
This heading has already appeared earlier with a slight difference in wording (Chapter: 105). In this instance, only the addition of putting a collar on the sacrificial animal is mentioned, meaning it is not necessary that the sacrificial animal be brought from home with a collar; rather, this Sunnah can also be practiced by purchasing the animal along the way.

(2)
In this narration, the Hajj of the Haruriyyah is mentioned. Harura is the name of a village near Kufa where the first gathering of the Khawarij took place; hence, they are called Haruriyyah. The Hajj of the Khawarij occurred in 64 AH, and the year when Hajjaj ibn Yusuf intended to fight Abdullah ibn Zubair radi Allahu anhu was the incident of 73 AH. It is possible that the narrator applied the term Khawarij to Hajjaj and his followers, because the government of Abdullah ibn Zubair radi Allahu anhu was legitimate, and Hajjaj rebelled against it and withdrew from his obedience. It is also possible that this incident occurred multiple times with Abdullah ibn Umar radi Allahu anhu.

(3)
It should be noted that Abdullah ibn Umar radi Allahu anhu did not face any kind of apprehension; rather, he performed all the rites of Hajj in a timely manner. (Fath al-Bari: 3/695)