Not necessarily. India for example was ruled primarily by Muslim rulers for over a thousand years but still ended up with a huge Hindu population and a significant Muslim population. If you consider the whole of South Asia, that "Diversity" in religion is even more stark. Since this region has almost 2 Billion people living, it can't be considered as different.
At the same time, you do have a good point. When you consider colonialism, what it represented was non-assimilation. One criticism of British Colonialism in India has been that unlike other Invasions (Greeks, Persians, Central Asian etc..), the British never did assimilate into India. The Mughals for example were conquerers from Central Asia (descendants from Mongols), but dropped their ties and forged new ones in India. That never happened in Colonialism not just by the British but every Colonial power. So, in that sense you are right about assimilation but its a bit more complex than that.
> India for example was ruled primarily by Muslim rulers for over a thousand years
Factually incorrect. India as a whole (esp. south India) was never under complete Islamic rule, let alone for a 1000 yrs. The Delhi Sultanate started around 1200 and British colonialism around 1700. That's around 500 years of Muslim rule esp. in north India.
The India you're talking about starts in what we today call Iraq and ends about 1/3rd into what we currently call India, encompassing Iran, Afghanistan, Pakistan and Bangladesh, and never reached the south of India or Madagascar. That was the area ruled by the Mughals, which was called India because, well it was. Their rule can be described as having a death toll of between 30 and 50 world war IIs.
The area of the Mughal empire is most definitely both religiously and ethnically cleansed. So it the other side. Before islam northern africa was black. In all likelihood, Hannibal was black.
There is no assimilation. Now in this case is was because of constant massacres, perpetraded predominantly by the muslim side (but where one side starts massacring, revenge will come).
But it doesn't really matter. The European conquest of the Americas has only a few massacres, certainly not comparable to what happened in Northern Africa or India. For the most part Native American culture dissappeared because, well, frankly, because Native Americans preferred European culture above their tribes (and in a lot of cases, they didn't have much of a choice, having lost a duel for leadership, or a woman, according to several monks who wrote on the subject). You see the same in places where "natural" human communities still exist, like sub-saharan Africa.
Just talk to the people there. You will note that they know life in the "villages" as they call it. They're not talking about some faraway town with a church but no supermarket (for one thing, they're not all that far from the cities, only 10km or so). They're talking about huts, hunting, and so on. They also know why the men leave (the women, well, mostly can't. Think about the impact on the group for 5 minutes and you'll understand why men can leave and women can't. And no, they're not prudes, the women can fuck whoever they want, kids are the village's kids, not really having any real mother or father, just a group of people who care for them (mostly the older children)). They are voluntarily abandoning the culture they have en-masse to attempt (and mostly fail) to join the third world. Having been there, I can certainly see why. Plus sometimes they get into trouble (e.g. lose a territorial battle, get half the tribe infected, run out of food, ...) and they have no choice.
At the same time, you do have a good point. When you consider colonialism, what it represented was non-assimilation. One criticism of British Colonialism in India has been that unlike other Invasions (Greeks, Persians, Central Asian etc..), the British never did assimilate into India. The Mughals for example were conquerers from Central Asia (descendants from Mongols), but dropped their ties and forged new ones in India. That never happened in Colonialism not just by the British but every Colonial power. So, in that sense you are right about assimilation but its a bit more complex than that.