The hell, respect the old culture? They couldn't completely stamp it out, more like it, but there was no respect there. Some native culture survived despite the Spaniards' attempts, but there was no respect whatsoever. The closest thing to "respect" was stuff like Bartomolé de las Casas thinking that it was cruel to enslave the natives because they weren't strong enough, so it would be better to bring Africans to America and enslave them instead (which he later also regretted, but the damage was done).

I don't even know where could you have possibly gotten the idea that the Spaniards were respectful. Were you told the Leyenda Rosa in school?

https://en.wikipedia.org/wiki/White_legend