Guys
How about that the EIC and later the British government don't discourage Christian evangelism and as a result there are large scale conversions from the lower castes and untouchables. Coupled with a continuation of the more flexible attitude to race by the earlier British rulers in the region.
As a result there is a significant element in India that identifies strongly with Britain, possibly aided by a stronger desire in the British leadership to win over the locals. The event that led to the mutiny, the declining economic and social status of the traditional Indian military castes, will still occur and probably be heightened by the presence of a considerable number of anglicised Indians. Especially as those, many from traditional low castes, increasingly take over roles in local government.
As such those populations will suffer heavily in the initial massacres by the rebels but their loyalty will help defeat the mutiny earlier, meaning their seen as a valuable bulwark against disloyal elements in the population. This means that they will gain further support from the authorities while the defeat of the traditional power elements will discredit them.
You get the steady accumulation of a growing proportion of the Indian population that identify themselves as British. Since they have access to better education and social links with the ruling elite they also have a growing prominence in the Indian economy, which also develops more as the influence of the 'Anglo-Indians' helps to modernise. Possibly also more influence in Britain with more Indian MPs in parliament, helping to represent their old as well as their new homelands.
As such you might find a fairly deeply divided India with a significant element sticking to traditional viewpoints and lifestyles, which however leave them increasingly sidelined. The new would be movers and shakers follow the more Anglo-Indian line in part because that has been shown as the best way of obtaining power and influence in the Raj. Probably richer overall and with a weaker caste system apart from those who still cling to it. As such less of a clear identity and maybe prone to internal clashes. However possibly as a result other conflicts are less prevalent. For instance religious conflicts might be muted because the Anglo-India/Nativist split divides all of those groups.
How this India relates to itself and Britain and the rest of the empire is difficult to tell. Very likely some clashes and differences at some point but hopefully better relations overall.
Steve