Answer:
Regarding the issue of Bay`ah or in English “Pledge of allegiance”, it was not recorded in history that women gave allegiance to the Caliphs, usually it is Ahlul-Hall wal-`Aqd who give the pledge then the women and children just follow along, what is meant by Ahlul-Hall wal-`Aqd are the leaders of the society, and it is common knowledge that the leader of the Islamic society at that time were the closest companions of The Prophet (SAWS), the Mouhajirun and the Ansar and they all gave Abu Bakr (ra) a pledge of allegiance.
Aside from the fact that women do not give a pledge of allegiance, In Islam not every single person is required to go and give the pledge of allegiance, so for the women it was enough that their husbands or male relatives or tribal leaders went and gave a pledge of allegiance, also there was no need for every single man to go and give a pledge and put his hand in the hand of the Caliph.
Let us give an idea to the readers, of what we are talking about, let’s say that the tribe of bani Hanifa in the land of Hijaz had a population of 5,000 people, and let’s say that they wanted to give allegiance to Abu Bakr (ra), does it means that the entire tribe of 5,000 men, women and children would travel all the way to Madinah, and each of them would give Abu Bakr (ra) allegiance and place their hands in his hand one by one? That is unheard of in Islam, what actually happens is that each tribe would send some representatives, maybe 13 men, maybe 4, and these men who are considered the leaders of those tribes would then give allegiance to Abu Bakr (ra), as for distant lands let’s say for example in the city of Kufa in `Iraq there would be a governor appointed by the Caliph, and the leaders of each tribe in `Iraq would meet up with this appointed governor and give him allegiance.
So for Fatima (ra) and all other women from bani Hashim, it was enough that the head of the family would go and give Abu Bakr (ra) allegiance, that would basically mean that all of them gave allegiance. And we know `Ali (ra) was appointed as head of bani Hashim, he was responsible for their affair and he gave Abu Bakr (ra) a Bay`ah.
And `Ali (ra) gave Abu Bakr (ra) Bay`ah(allegiance) on the very first day as is recorded in the authentic narration:
Abu Sa’eed al Khudri may Allah be pleased with him said: When the Prophet’s (SAWS) soul passed away and when the people gathered at the place of Sa’ad bin Ubadah and amongst them were Abu Bakr and `Umar, a Khatib(Speaker) from the Ansar(Supporters) spoke: “You know that the Prophet of Allah (SAWS) was from the Mouhajirun(immigrants) and his Caliph(Successor) must also be from the Mouhajirun, we were the supporters of the Prophet (SAWS) and we will be the supporters of his successor(Caliph) just as we were his supporters”. then `Umar bin al Khattab stood up and said: “This Man from amongst the Ansar speaks truth, and if it were anything other than this then we would not give you a bay’ah(Pledge of allegiance).” Then he grabbed the hand of Abu Bakr and said: “This is your close companion so give him Bay’ah.” Then `Umar and the Mouhajirun and the Ansar all gave him Bay’ah. Abu Bakr stood on the Mimbar and he looked at the faces of all the people there but he never saw al-Zubair so he called for him and and he came so he told him: “O son of the Prophet’s (SAWS) aunt and his disciple would you want to split the cause of the Muslims?” al-Zubair said: “Not at all O Caliph of the Prophet of Allah.” then he stood up and gave him Bay’ah, Then he looked at the faces of the people again but did not spot `Ali so he called for `Ali bin abi Talib and he came to him so he said: “O cousin of the prophet of Allah and the husband of his daughter would you want to split the cause of the Muslims?” So `Ali replied: “Not at all O Caliph of the Prophet of Allah.” then he stood and gave him Bay’ah.
sources:
-Mujama’a al Zawa’ed (5/183) with its Rijal being those of the SAHIH.
-Al Bidayah wal nihayah (5/281) with its Isnad being Thabit and SAHIH.
-Al Mustadrak (3/76) and al Sunan al Kubrah (8/143) with two SAHIH Isnads.
So we came to know that, in the case of Fatima(ra) it was her husband(ra) who gave a pledge of allegiance to Abu Bakr (ra) and she just followed along, the Caliphs never demanded or asked for the pledge of allegiance from women, so whether she went or didn’t go doesn’t matter.
Moreover, We read in an authentic narration from “Ithaf al-Khayarah al-Maharah” by al-Bouwaysiri, that
وَقَالَ أَبُو يَعْلَى الْمُوصِلِيُّ حَدَّثَنَا عَبْدُ الرَّحْمَنِ بْنُ صَالِحٍ ، حَدَّثَنَا مُحَمَّدُ بْنُ فُضَيْلٍ ، عَنِ الْوَلِيدِ بْنِ جُمَيْعٍ ، عَنْ أَبِي الطُّفَيْلِ ، قَالَ : جَاءَتْ فَاطِمَةُ إِلَى أَبِي بَكْرٍ ، فَقَالَتْ : يَا خَلِيفَةَ رَسُولِ الله.
Abi al-Tufayl said: Fatima came to Abu Bakr and said: “O Khalipha of Rasool-Allah (SAWS)…
This is a clear proof that like her husband(Ali) and the rest of believers, even Fatima(ra) accepted Abubakr(ra) as the Khalipha of Prophet(saw). Had it been that she didn’t accept Abubakr(ra) as the Khalipha, she wouldn’t have used those terms, since we know that dignified Arabs would never call a person with a sacred title, unless they truly believe that the person deserves that sacred title. For example, Suhail bin Amr who was a disbeliever at the time of treaty of Hudaibiyah, didn’t allow Muslims to write the words “(Messenger of Allah)” after name Muhammad(saw) in the treaty. So how could Fatima(ra) the leader of women in paradise call Abubakr(ra) Khalipha of Rasool Allah, if she don’t consider him to be so.
Also one of the biggest scholars of the Muslims and Fatima’s (ra) great-grandson Muhammad bin `Ali stated that he does not know of anyone from his family was not loyal and obedient to Abu Bakr (ra), it is narrated:
from Bassam bin `Abdullah al-Sayrafi: I asked Abu Ja`far(al-Baqir): “What do you say about Abu Bakr and ‘Umar may Allah be pleased with them?” He replied: “By Allah I am loyal to them and I ask Allah to forgive them and we never knew anyone from our family who was not loyal to them.“ (“Fadael al-Sahaba wa Manaqibihim wa Qawl Ba’adihim fi Ba’ad” by al-Imam al-Darqutni.
grading: Hadith Hassan(good).
Based on the above the matter is as clear as daylight. Fatima(ra) was pleased with Abu Bakr(ra) and loyal to him and so was her entire family, how can she not be pleased with the beloved companion of her father (SAWS)?
Thus, as for Fatima(ra) giving Abubakr(ra) a pledge of allegiance or a Bay`ah, this is not required from women in Islam and we have never read any Caliph demanding women to offer such a pledge. Moreover, it was never recorded in any instance that Fatima (ra) disobeyed Abu Bakr (ra).
Moreover, the report from Sahi bukhari, which states that Fatima(ra) was angry and didn’t speak to Abubakr(ra) until she died, is usually used by Shias to assume that Fatima(ra) didn’t give allegiance to Abubakr(ra), but the fact is that this report is from the idraaj(interpolations) of famous narrator Zuhri, who was criticized for interpolations. The part which Shias use from the hadeeth is from his interpolations, because he misunderstood and equated silence with anger. A detailed research has been done in our article on this subject where we have proven that, this part is not reliable. (Refer this link).
Secondly even if supposedly one accepts this unreliable interpolation then too, this is not a proof that Fatima(ra) removed herself from obedience to Caliph Abubakr(ra). It would be considered as a disagreement between them, and the history is filled with cases where people disagreed with the decision of their Caliphs, but this doesn’t imply in any way that they refused to give allegiance nor that they broke their allegiance. Especially, when we know the noble character of Fatima(ra) and Abubakr(ra), as these were the people who never preferred worldly possessions over the hereafter. It’s in fact thinking low of Fatima(ra), that because of a worldly possession(land of fadak), Fatima(ra) didn’t give allegiance or broke it. Imam Ahmed bin Hanbal(rah) was tortured by the Caliph of his time, but this doesn’t implies that He broke allegiance from the Caliph. These are assumptions of Shias which has no basis.
https://youpuncturedtheark.wordpress.com/2014/01/29/hadeeth-explanation-whoever-died-without-an-imam-he-dies-a-death-of-jahilyyah/