The main way that you can see this as a religious crusade is because it was fought, in large part, to get the Muslims (the Moors) out of Spain.
Before the Moors were driven out of Spain, Spain was not a country (a united one) like it now is. Instead, there were all sorts of smaller divisions of what is now Spain. Some of the bigger divisions were united when King Ferdinand and Queen Isabella married, bringing their kingdoms together.
The rest was brought together when they drove the Moors out of Spain. At that point, what is now Spain became unified and Christian instead of split and part-Muslim (and part Jew, as Isabella drove the Jews out of Spain).