What is the ruling on preferring one rightly-guided Caliph over another rightly-guided Caliph who preceded him, such as (preferring) Umar, may Allah be pleased with him, over Abu Bakr, may Allah be pleased with him, and does prohibition apply here?

The best of this Ummah after its Prophet Muhammad, peace and blessings be upon him, is Abu Bakr, then Umar, then Uthman, then Ali, then the rest of the ten who were given glad tidings of Paradise, then the people of Badr, then the people of the Pledge of Ridwan, then the people of the Conquest (of Mecca), and then those Companions who came after them. This is the position of the Ahl al-Sunnah wal Jama'ah. Whoever prefers Umar or anyone else over Abu Bakr Al-Siddiq has erred and innovated.

Evidence for Abu Bakr's virtue has been successive from the Qur'an, the Sunnah, and the consensus of the Ummah, such as the Almighty's saying: ﴿If you do not aid him, Allah has already aided him when those who disbelieved expelled him, he being the second of two; when they were in the cave and he said to his companion, "Do not grieve; indeed Allah is with us."﴾ [At-Tawbah: 40]. His companion is Abu Bakr, by the consensus of the exegetes. He also possessed unique characteristics not found in others, such as the Prophet's saying, peace and blessings be upon him: "Had I taken a close friend from among the people of the earth, I would have taken Abu Bakr as a close friend," and his saying: "Let no window remain open in the mosque except the window of Abu Bakr," and his saying: "Indeed, the most generous of people to me in his companionship and his wealth is Abu Bakr." Based on this, it is not permissible to prefer any Companion over Abu Bakr, may Allah be pleased with him.