The ironic consequence of this fact is that oftentimes, a pair of Catholic royals would actually be most closely related through Protestant ancestors. Prince-Regent Luitpold of Bavaria (born 1821) and his wife, Archduchess Augusta Ferdinand of Austria-Tuscany, for instance, were only fifth cousins, once removed. His brother (Prince Adalbert) and sister-in-law, Infanta Amalia of Spain, were only fifth cousins.
The distant relationships between the couples are all the more remarkable, considering that all parties were Catholics with completely royal ancestry for several generations. But perhaps this is no surprise: Bavaria used to be only a duchy whose population was 90% Catholic. But it eventually grew into a kingdom, as it gained more territories (thanks to Napoleon). So the religious demographics changed, and became 2/3 Catholic. In a spirit of solidarity, in order to extend a hand of courtesy to the Protestant population, the Catholic sovereigns of the new kingdom of Bavaria deliberately sought out Protestant princess brides for marriage.
Thus it was that Infanta Amalia of Spain, who came from the Bourbon stock of intermarriages among the royal dynasties of Spain, Parma, and the Two Sicilies, was not very closely related to her husband, who came from the stock of German royals, Catholic and Protestant. Of course, in the next two generations, there would be closer cousin marriages between the Bourbons and Wittelsbachs ...
Interestingly enough, King Maximilian II of Bavaria and his Protestant-born consort, Princess Marie of Prussia, were more closely related as third cousins. As it was, Queen Marie was related to both wives of her husband's grandfather (King Maximilian I) -- Princess Augusta of Hesse-Darmstadt and Princess Caroline of Baden. That would explain her ties to the royal house of Saxony and imperial house of Austria, among others.
However, I wish to focus only on fully Catholic couples (Marie converted to Catholicism only later on, after her husband's death) who were not very closely related.
Can anybody name other examples of such? Please be sure to list only those persons who had completely (or nearly completely) royal ancestry. It's interesting to note that even if one is not necessarily talking about married couples, one can randomly pick a pair of Catholic royals most closely related through Protestant ancestors. "Mad" King Ludwig II of Bavaria and Archduchess Maria Theresia of Austria-Este (who married his first cousin, the future King Ludwig III) were fourth cousins, once removed, as descendants of King Friedrich Wilhelm I of Prussia and Sophia Dorothea of Hanover (daughter of King George I of Great Britain).