It's worth remembering that the Ottoman conquests occurred hundreds of years before the Armenian Genocide (which, if you include earlier mass-killings of Christian minorities you could plausibly date to the end of the 19th century.)

It would simply never have occurred to a group of people who were conquering whole swathes of Christian territory that this one particular group of Christians would be viewed as an internal enemy that needed to be eliminated by their descendants hundreds of years later.

Muslims were a numerical minority in the Ottoman Empire until the Mamluk war of 1516-17. There was little to no sense that the empire should be entirely Islamic: conversion was valued, but only when sincere.

To get more into your question, the Ottoman Empire used different groups (such as Christian communities in the Balkans) as units for administration. Have a look at Karen Barkey's Empire of Difference if you're really interested in this. Connections were made between existing elites and Ottoman administration, strengthening these communities. The Ottoman empire was a patchwork of diverse communities- and belonging to the empire arguably strengthened the differences between some of these communities as much as it brought them together under a common cause.

Interestingly, it is very possible to argue that, under the first centuries of the Ottoman Empire, the Balkans were a more ethnically and harmonious place than towards the end and since. The basis of legitimacy of the Empire changed throughout the six centuries, and towards the end, became far more a 'nation-state' in terms of it's exclusivity. The earlier centuries of Ottoman rule, though by no means fabulous for non-Muslim communities (who were, for example, given special taxes) were relatively diverse. Co-existence isn't and wasn't unnatural to most communities.