Short answer
With love, respect and gratitude, together with love for the Prophet's (ﷺ) family. Allah (﷾) praises the first Muslims and says He is pleased with them. The Prophet (ﷺ) told us not to abuse his companions. Ali loved them too. Asked who was best after the Prophet (ﷺ), he named Abu Bakr and then Umar, and he asked Allah's (﷾) mercy for Umar when he died. We love Ali, Fatima, al-Hasan and al-Husayn, and we love the companions. We do not set the family against them. Whatever passed between them, we leave to Allah (﷾). Everything we know of the Qur'an and the Sunnah reached us through them.
Full explanation
What Allah (﷾) says about the first Muslims
The Qur'an speaks of the first emigrants, the helpers who received them, and those who followed them in good. Allah (﷾) is well pleased with them, and they with Him. When the believers swore loyalty to the Prophet (ﷺ) under the tree at Hudaybiyya, Allah (﷾) says His good pleasure was on them. He knew what was in their hearts. He also describes the Prophet's (ﷺ) companions as strong against disbelief and compassionate among themselves, and promises forgiveness and a great reward.
“The vanguard (of Islam)- the first of those who forsook (their homes) and of those who gave them aid, and (also) those who follow them in (all) good deeds,- well-pleased is Allah with them, as are they with Him: for them hath He prepared gardens under which rivers flow, to dwell therein for ever: that is the supreme felicity.”
“Allah's Good Pleasure was on the Believers when they swore Fealty to thee under the Tree: He knew what was in their hearts, and He sent down Tranquillity to them; and He rewarded them with a speedy Victory;”
“Muhammad is the messenger of Allah; and those who are with him are strong against Unbelievers, (but) compassionate amongst each other. Thou wilt see them bow and prostrate themselves (in prayer), seeking Grace from Allah and (His) Good Pleasure. On their faces are their marks, (being) the traces of their prostration. This is their similitude in the Taurat; and their similitude in the Gospel is: like a seed which sends forth its blade, then makes it strong; it then becomes thick, and it stands on its own stem, (filling) the sowers with wonder and delight. As a result, it fills the Unbelievers with rage at them. Allah has promised those among them who believe and do righteous deeds forgiveness, and a great Reward.”
The prayer Allah (﷾) teaches those who come after
Allah (﷾) describes three groups: the poor emigrants, the helpers who gave them preference over themselves, and "those who came after them". The last group is us. Allah (﷾) gives us a prayer to say. We ask forgiveness for ourselves and for our brethren who came before us in faith. We ask that He leave no rancour in our hearts against the believers. That prayer is part of the Qur'an.
“(Some part is due) to the indigent Muhajirs, those who were expelled from their homes and their property, while seeking Grace from Allah and (His) Good Pleasure, and aiding Allah and His Messenger: such are indeed the sincere ones:- But those who before them, had homes (in Medina) and had adopted the Faith,- show their affection to such as came to them for refuge, and entertain no desire in their hearts for things given to the (latter), but give them preference over themselves, even though poverty was their (own lot). And those saved from the covetousness of their own souls,- they are the ones that achieve prosperity. And those who came after them say: "Our Lord! Forgive us, and our brethren who came before us into the Faith, and leave not, in our hearts, rancour (or sense of injury) against those who have believed. Our Lord! Thou art indeed Full of Kindness, Most Merciful."”
What the Prophet (ﷺ) said about them
The Prophet (ﷺ) said: do not abuse my companions. If one of you spent gold as great as Mount Uhud, it would not reach what one of them gave, a mudd, about a double handful, or even half of it. He also said the best of people are his own generation, then those after them, then those after those. These reports are in Sahih al-Bukhari.
Abu Said al-Khudri reports that the Prophet (ﷺ) said: do not abuse my companions. If any of you spent gold as great as Mount Uhud, it would not reach a mudd, or even half of one, of what one of them spent.
Abdullah ibn Mas'ud reports that the Prophet (ﷺ) said the best of people are his own generation, then those who follow them, then those who follow the next.
What Ali said about them
Ali's own words are the best guide. His son Ibn al-Hanafiyya asked who was best after the Messenger of Allah (ﷺ). Ali answered Abu Bakr, then Umar. When the son asked, then you? Ali said he was only a man among the Muslims. When Umar died and his body was laid out, Ali came and asked Allah's (﷾) mercy for him. He said no one's deeds were dearer to him to meet Allah (﷾) with than Umar's. Ali's daughter Umm Kulthum was Umar's wife.
Ali's son Ibn al-Hanafiyya asked his father who the best of people were after the Messenger of Allah (ﷺ). Ali answered Abu Bakr, then Umar. Afraid that Ali would name Uthman next, he asked: then you? Ali replied that he was only a man among the Muslims.
Ibn Abbas reports that when Umar's body was laid out and the people prayed for him, Ali came, asked Allah's mercy for Umar and said that no one's deeds were dearer to him to meet Allah with than Umar's. Ali said he had always thought Allah would place Umar with his two companions, because he often heard the Prophet (ﷺ) say: I, Abu Bakr and Umar went; I, Abu Bakr and Umar entered.
Umar divided garments among the women of Medina, and one good garment was left. A man told him to give it to his wife, the granddaughter of the Messenger of Allah (ﷺ), meaning Umm Kulthum, the daughter of Ali. Umar gave it to Umm Salit instead, a woman of the Ansar who had carried water-skins for the Muslims at Uhud.
The family and the companions loved each other
Abu Bakr lifted the child al-Hasan onto his shoulders and said he looked like the Prophet (ﷺ), not like Ali, while Ali smiled. He told the people to honour Muhammad (ﷺ) by honouring his family. At Khumm the Prophet (ﷺ) himself told the people to hold fast to the Book of Allah (﷾). He reminded them of their duty to his household. Loving his family and his companions is one love, not two.
Uqba ibn al-Harith reports that after the Asr prayer Abu Bakr saw al-Hasan playing with the boys and lifted him onto his shoulders. He said: you look like the Prophet (ﷺ), not like Ali. Ali was smiling.
Abu Bakr said: watch over (honour) Muhammad (ﷺ) through his family.
Zayd ibn Arqam reports that at a watering place called Khumm, between Mecca and Medina, the Prophet (ﷺ) praised Allah and said he was leaving two weighty things among the people: the Book of Allah, which holds right guidance and light, so hold fast to it; and the people of his household, reminding the people of their duties to the members of his family. Zayd said the Prophet's (ﷺ) wives are of his household, but the household meant here are those to whom charity is forbidden: the family of Ali, of Aqil, of Ja'far and of al-Abbas.
Why it matters
The Qur'an reached us through the companions: they heard it, memorised it and passed it on. The Sunnah came the same way. Among them were Ali and the Prophet's (ﷺ) family. Allah (﷾) promised to guard the Qur'an. If we treat those who carried it with contempt, we weaken our own trust in what they carried. And the Prophet's (ﷺ) example was mercy, not cursing.
“We have, without doubt, sent down the Message; and We will assuredly guard it (from corruption).”
Abu Hurayra reports that someone asked the Messenger of Allah (ﷺ) to curse the polytheists. He answered that he had not been sent as one who curses, but as a mercy.
Abdullah ibn Mas'ud reports that the Prophet (ﷺ) said the best of people are his own generation, then those who follow them, then those who follow the next.
Perspectives
Some Muslims believe some companions went astray and may be criticised
Some Muslims, from love of the Prophet's (ﷺ) family, hold that certain companions turned away after the Prophet (ﷺ) and wronged his family. They believe that honest faith includes naming this. They bring these arguments.
The Prophet (ﷺ) said some of his companions would be driven away from the Lake-Fount. It would be because of what they did after him.
Rebuttal
The report speaks of "a group" and names no one. Allah's (﷾) pleasure is on the believers who pledged under the tree, and Ali, Abu Bakr and Umar were with the Prophet (ﷺ) at Hudaybiyya. What Allah (﷾) says about the believers there is not cancelled by a report that names no one.
Some people around the Prophet (ﷺ) were hypocrites, so we cannot trust all of them.
Rebuttal
The same verse says the Prophet (ﷺ) did not know them, but Allah (﷾) did. We cannot name them, and we are told to avoid suspicion. We trust what Allah (﷾) said of those He praised.
Honest history means naming the wrongs of the early community, and silence would be injustice.
Rebuttal
Allah (﷾) says of earlier peoples that they have what they earned, and you will not be asked about what they did. Ali himself asked Allah's (﷾) mercy for Umar and named Abu Bakr and Umar the best.
Loving the Prophet's (ﷺ) family means distancing ourselves from those who opposed them.
Rebuttal
The Prophet (ﷺ) asked for love and care for his household and for his companions. He said he was sent as a mercy, not as one who curses. Ali's own words show that love of both is one.
The Islamic perspective
Muslims love all the companions, the Prophet's (ﷺ) family among them. Allah (﷾) is pleased with the first believers, the Prophet (ﷺ) forbade abusing them, and Ali himself honoured them. What passed between them is left to Allah (﷾).
Allah (﷾) is well pleased with the first emigrants, the helpers and those who followed them in good.
Allah (﷾) teaches believers to pray for those who came before them and to keep rancour out of their hearts.
The Prophet (ﷺ) forbade abusing his companions.
Ali named Abu Bakr and Umar the best after the Prophet (ﷺ). When Umar died, Ali asked Allah's (﷾) mercy for him.
Love for the Prophet's (ﷺ) family and love for his companions belong together.
What passed between the early Muslims is left to Allah (﷾).