It was only 25 years after the demise of the Prophet of Islam (S) that the Muslim caliphate got back on its original track. After coming to power and becoming apparently a caliph, Imam Ali (AS) vowed to do away with all the innovations that had come into being until then.  But this long period was enough for Muslims to get used to the manners and etiquettes which were introduced to them in the name of the Messenger of Allah (S) and his successors.
During this time period, the Islamic government developed and expanded extensively and these innovations found their way into the entire Islamic territories and lands. Nevertheless, Imam Ali's efforts to eliminate innovations did not stop. At times, for a larger interest of the Islamic society and to prevent discord and sedition, he would not embark on any action.
One of the innovations (bid'ah) promoted during the time of the second caliph and which was initiated by him was 'folding hands during prayers'.[1] As well, the sentence "al-Salat khayrun min an-Nawm" (prayer is better than sleep) was added to the Fajr Adhan and the declaration "Hayya 'alaa khairil 'amal" was removed from it.[2]
Allamah Majlisi (ra) has dedicated a section of his book to this topic explaining why the Commander of the Faithful, Imam Ali (AS) did not reverse some of the innovations in his time.[3] He points out some of the hindrances and obstacles to the combat against the innovations.
Late Kulayni (ra) makes mention of a lengthy narration and narrates Imam Ali's sermon about the innovations and why he did not take action to change them. The narration is interesting to read:
"The caliphs before me deliberately opposed the Messenger of Allah doing things that led to alteration of his tradition (sunnah). Should I embark on stopping people from what they have innovated and make them adopt the tradition of the Prophet (S), no army will remain for me, except myself and a few of followers…".
Thereupon, Imam Ali (AS) makes mention of most of the innovations and concludes:  Did you see that when I stopped them from performing Taraweeh (mustahab prayers which Sunnis perform in jama'at), some of those who fought alongside me in my army shouted, "O Muslims, Umar's tradition is gone" and the army was going to fall apart and follow the leaders of misguidance.[4]
This is Imam Ali's grievance and complaint which somehow give us an illustration into the Muslim society of his time as well as of Muslims who knew nothing about the difference between tradition and innovation nor about those who deliberately embarked on derailing the prophetic society and putting it on a wrong track. The Ummah (people) of his time identified themselves largely as a nation practicing those innovations and made no difference between Ali (AS) and those before him; rather they preferred the previous caliphs over him because of their temporal precedence.
Therefore, Imam Ali (AS) fought all the innovations; he stood up against them and his opposition to those innovations have been documented in history. His special friends and companions also did not act upon those innovations as far as they could; they rejected the innovations and denied them but a large segment of the society did not follow suit. Not only they did not accompany the Commander of the Faithful in the fight against the innovations but they also opposed him.

[1] See: "Shi'ah and Performing Prayers with Open Hands, Folding Hands", question 3828.

[2] See: "Hayya 'alaa Khairil 'Amal", question 20111.

[3] Majlisi, Muhammad Baqir, Behar al-Anwar, vol.34, p.167, Beirut, Al-Wafa Institute, first edition, 1410 A.H.

[4] Kulayni, Muhammad bin Ya'qub, al-Kafi, researched and edited by Ali Akbar, Akhundi, Muhammad, vol.8, p.58, Tehran, Dar al-Kotob al-Islamiyyah, fourth edition, 1407 A.H.