Lets examine portuguese case: they engaged in forced conversions and aggression against everyone including even the nasranis. They tried their maximum to convert as many people as possible. Eventually even the christians/nasranis here could not tolerate them. And they got ejected by the dutch.
British case.....they tried conversions directly till 1857, when missionary excesses led Hindus and Muslims to unite against them.
Britishers may have been highly organized. But they were no mongols or mughals. If the hindus and muslims of the subcontinent sneezed together, the british would have landed in arabia. British colonials- around 80,000 to 2 lakh of them controlled the Indian subcontinent, through their sheer organisation skills and by recruiting locals. They could not risk letting missionaries scot free, as they
understood the risk of hindu muslim unity.