​ The Spanish definitely drew many parallels between (Iberian) Muslims and America's native populations. Rather than simply comparing, I would say that they perceived the previously unknown lands and their inhabitants in relation to what they knew from Europe. This meant especially applying institutions and negative views of the Muslims developed during the centuries-long Iberian "reconquista" to the new Spanish overseas possessions - in a variety of areas, incl. religion, law, and arts. I've written about this a bit before, hopefully between these answers you can get a better picture of this influential process - let me know in case of questions:

• A more general one, talking about literature and arts in colonial Mexico

• This one focused on the example of rituals known as cristianos y moros in Spain and central America

• On a different topic, but under point I.) I talk about the casta system, so Iberian judicial processes of exclusion brought to the Americas

As an intro to those I'm adding my conclusion from the 1st answer:

"the reconquista and its parallels with the crusades were extended to Ibero-America and transformed as important ideological features of early colonial life ... This intellectual transmission can be seen in literature and art (e.g. with St. James „mataindios“), but also in religious and territorial concepts (like the requerimiento). The transformation of these medieval concepts would continue in New Spain in different ways with the conquistadors' decreasing influence towards the mid-16th century, and increasing importance of religious orders and gradually of creoles."