With Spain being fervently Catholic didn't they view anything of Moorish origin as tainted or inferior?
The primary reason is that Moorish art and architecture had by that time become firmly entrenched as Spanish art and architecture. If you look at buildings from the late medieval through Baroque periods, both in Spain proper and in Latin America, there are clear mudejar influences--the arches and the tilework being two major features. In addition to (or really, prior to) copying Moorish styles, Christian Iberians also coopted existing buildings--perhaps mostly famously, the Mezquita of Córdoba that became the city's cathedral.
In short, Muslim architecture in Spain was not, by the 15th century, viewed as Muslim, but as local.