However, because of the absence of interfaith equal marriages with Catholic dynasties, the house of Orange has not had a strong claim to being related to the entire ALMANACH DE GOTHA.
By contrast, the first king of the Belgians was a Lutheran who married, as his second wife, a French Catholic princess (Louise of Orléans, daughter of King Louis-Philippe of the French). Marriages between the Coburgs of Belgium remained largely to fellow Catholics after that union.
But in 1926, the future King Leopold III married Princess Astrid of Sweden and Norway -- a Protestant, like King Leopold I. She was a niece of three Lutheran kings of Scandinavia.
Interestingly enough, she also descended from the Catholic Maximilian I Joseph, first king of Bavaria -- who was among the ancestors of Queen Elisabeth. She also descended from Eugène de Beauharnais, a second cousin of Stéphanie de Beauharnais -- who was among the ancestors of King Albert I. So the Protestant-born Astrid was related to both parents-in-law, themselves Catholics with Protestant ancestry (e.g. Coburg, Baden, Hesse-Darmstadt).
Astrid is the tying link between Scandinavia, Belgium, and Luxembourg; but the grand duchy also has a history of interfaith marriages and changes in religion. Don't forget that according to the treaty at the Congress of Vienna, it was to be ruled by the House of Nassau, which was Protestant. But in 1893, the future Grand Duke Guillaume IV (who like his father belonged to the Weilburg branch) married Infanta Maria Ana of Portugal, a Catholic with some Protestant ancestry herself (e.g. Princess Agnes of Hohenlohe-Langenburg).
So it's no surprise that Belgium and Luxembourg are well-connected. For although the Scandinavian sovereigns are fully royal in ancestry (more blue-blooded than the British queen, who has common and morganaut ancestry within three generations), marriages within those kingdoms have largely been to fellow Protestants. So their ties to the Catholic and Orthodox dynasties are only indirect (notwithstanding the fact that the present-day Greek dynasty is an offshoot of the Danish). I believe the nearest Catholic sovereign ancestor to the reigning monarchs of Norway, Sweden, and Denmark is the afore-mentioned King Maximilian I of Bavaria (thanks to the marriage of his daughter Augusta to a prince of Leuchtenberg: their daughter Josephine became a Catholic queen of Protestant Sweden).
Since members of the princely houses of Monaco and Liechtenstein, despite being sovereign dynasties, have largely married nobles over the years, the said principalities are not very well-connected. They may be related to the entire Gotha, but the relationships to the various houses are only distant.
So this means that the claim to having the closest relationships with the most houses listed in the Almanach probably belongs to either King Felipe VI of Spain or Grand Duke Henri of Luxembourg (like I said, he is better connected than his Belgian cousin, whose mother was born only an Italian noblewoman). Because King Juan Carlos is related to all the Catholic royals of Europe (in addition to having Protestant ancestry), and because Queen Sofia descends from Queen Victoria of Great Britain, King Christian IX of Denmark, Czar Nicholas I of Russia, and the kings of Prussia, I'd say that the Spanish king wins the contest.
Do you agree?