Nothing was so clear cut as that. When I studied early American history, even in early colonial times in the USA there were groups of mixed Natives + whites. One such group was massacred by a jealous Indian tribe. But today it is not at all uncommon to meet white people who are genuinely part native.

French and Spanish didn't simply try to convert the natives. They depended on them. And they also mated with them frequently. Does that mean these people are now more born into sin than the rest of us? I don't think so and history does not prove that.

Conquest is not a great thing, but it does happen. Mixing can also happen because of trade. If your region is an economic hub, like say Singapore or New York, it happens. Any nation that becomes a great empire will see people flocking towards it as well.