In the Balkans and Asia Minor, the Christians were treated as slaves and there were many who changed their religion so that they could join the Ottomans in ruling over the Christian population.

I'm not sure about this particular conflict or the role religion played in it but if religion played as significant of a role as you say it did, it would be an isolated incidence.

So, at least in parts of the Ottoman state, the distinction between slaves and non-slaves was based on religion, and the Christians were mostly white Europeans.

I don't think this video makes the case for this at all. I am not convinced this religious angle played as much of a role as you say it did. Look, I've seen so called "Muslim slavery" in the Arab world as it stands today and it is a simple truth that the targets of that so called "Muslim slavery" under the Khafala system are often poor brown Muslims at the hands of Arabs. There is more of an agenda to enslave poor Muslims from Africa and South Asia in the Middle East right now then there ever was to enslave white Europeans. Right now, any white European or American that goes to the Middle east gets paid lavishly and treated like royalty (as long as they abide by rules and customs) while the poor laborers from Africa and South Asia get held as slaves. I just don't see the desire to enslave any white people in the Middle East when the concept of white privilege is more applicable there than it has been in America in the past century. Either way, I say all this just to acknowledge that yes, the so called "Muslim slavery" you talk about is very real but to look at this through this lens of "Muslims want to enslave whitey" is just plain inaccurate and a reductive conception of what is actually going on here.