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Shuja of Lucknow participated in battle against Marathas for two reasons
1. Islamic brotherhood
2. Najib's threat of releasing abdali on Awadh
What marathas seriously misunderstood was rallying power of Islam as an idea and its efficacy in gangetic plains. The call of "Islam in danger" had no effect whatsoever on Telugu Ibrahimkhan Gardi who fought and died alongside Sadashivrao Bhau on the fields of Panipat. It had effect only on Muslims in Gangetic plains. This thing repeated during rise of Muslim leage in decade of 1940s. The idea of Pakistan did not have much support amongst Muslims in Punjab, Bengal and rest of India. It was primarily in Muslim majority districts of UP and Bihar.
Marathas considered Gangetic valley as temporarily fixed with bengal in disarray and friendly Shuja. 1755 OR 1756 to be more precise is the period of Adina Beg's idea of granting Punjab's rights to Marathas in exchange of their promise to protect Delhi from Pathans. This is when the lobbying and deliberations began. When capable people are at helm, they see things coming much earlier. In spite of whatever people say, Nanasaheb and Sadashivrao bhau were extremely capable administrators and statesmen.
The problems for Marathas started in 1737, when Bajirao-1 conquered Delhi. It was his decision not to oust Mughal emperor. He should have made himself as king of delhi OR made shahu chhatrapati as Dillipati. This was the moment of choice. When Bajirao-1 decided to preserve Mughals for namesake, the die was cast. The alienation of Hindu kings (mentally) started from that moment itself. The emotional pull of idea of Shivaji's Hindavi swarajya ended with this choice of Peshwa.
Why did Marathas preserve Mughals?
The decision of preserving Mughal emperor for namesake is most intriguing of all the decisions of Marathas. If one starts blaming Marathas for that decision, one is intrigued that when staunchly anti-Mughal Sikhs conquered Delhi temporarily in 1770, even they did not choose to oust Mughal emperor and declared him titular head. Until 1803, Mughal emperor was titular head while living off the pension from Marathas. After 1803, the guardianship of Mughal emperor moved to East-India Company when even they continued this policy of Bajirao-1 Peshwa of keeping Mughal emperor as nominal head.
Mughal Empire was non existent and in rapid decline since 1703 when Marathas crossed Narmada and conquered central India. Yet, Mughal dynasty continued to linger on till 1857 due to their preservation by Marathas and East India company respectively. Even while 1857's Indian war of independence, Nanasaheb -2 Peshwa and Tatya Tope tried to replicate similar model by naming old Bahadur Shah Zafar as titular head of independent India.
The Mughals had a large supporting networks in terms of marriage, shared unbroken blood lines and of course basic religious philosophical motivations with "all" the Islamic pieces of the Mughal empire which had survived despite the Mughal power falling.
Once a power base is created, it is not merely the dynastic people at head, which as we see in case of last Mughals were personally vacuous and inept. It is the inertia of the mutually benefiting groups which continue to need the "name" to keep the network going.
The Maratha's chose to use the network to their advantage rather than pick a fight with everyone at once by breaking it -- of course in hindsight we know it is wrong decision -- and they should have made their own ideological allies -- but in reality could they? As a large centrist power whose cadre was drawn from ALL quarters?
Having made the choice to preserve Delhi and Mughals in 1737, the requirement of Marathas in terms of "allies" changed. This is what culminated in their decisions in 20 years later. Those who could have been long term allies were alienated because of this decision.
In changed scenario of requirements, the players who presented themselves as potential allies had their advantages and drawbacks.. Whilst Marathas appreciated the advantage of preserving mughals and hence support of shuja while ignoring Jats, they did not appreciate the drawback of the same. The context of this policy realignment in 1750s is in the decision of 1737..
Once they decided to preserve delhi (an inherently islamic power centre) the responsibility of preserving and protecting other allied islamic power-centres fell upon them too. This is the reason they could not eliminate Nizam of hyderabad, in spite of defeating him conclusively time and again. Najib was Persona non grata because he openly aspired to overthrow Mughals and sit on throne himself.
Marathas left deccan to overthrow Mughals. By the time they reached Delhi, they became protectors of Mughals. This was a "deal-breaker" for many other people (like Sikhs, Jats, Ahoms) who were fighting against Mughals previously.