The royal families of Liechtenstein and Belgium are Catholic. The Russian royal family were and the Greek royal family are not Roman Catholic but Orthodox Catholic, definitely not Protestant.
Whether on the throne (Spain, Liechtenstein, Belgium, Luxembourg, Monaco) or 'temporarily' off the throne but still around (Italy, Greece, France, Portugal, Bulgaria, Hungary, Austria), the majority is Catholic.
All the major long running royal families are for logical historic reasons Catholic. They were either formed in a time when Catholicism was the only thing or formed in a region where Catholicism still is the only thing. All the big names, Habsburg, De Bourbon, D'Orleans, House of Savoy, Hohenzollern etc. have a long Catholic tradition.
Most of the protestant royal families (Netherlands, UK, Denmark, Norway) are offshoots of German princedoms. That's where the reformation took place and where, obviously, the first Protestant royals came to be.
There have been some changeovers and splits, though. The Protestant House of Luxembourg-Nassau switched to Catholicism as Luxembourg’s population was overwhelmingly Catholic. The members of the House of Sachsen-Coburg und Gotha who sit on the Belgian and British throne consider themselves Catholic in Belgium but Protestant in the UK.
Anyway, my point was that, despite most royal families being Catholic which might have limited the choice of partners for Protestants, inbreeding has not been an issue among Protestant royals because of the abundance of Germans with 'blue blood'.