No: none of the reigning European monarchies requires any religious marriage for the union to be valid (and dynastic) under law. Only the British crown is linked to an official church; but even in the UK, the Earl of Saint Andrews was able to civilly wed Sylvana Tomaselli and still ensure that his marriage was dynastic.
A civil marriage suffices anywhere, as evidenced by the 1983 wedding of Princess Caroline of Monaco and her second husband, Stefano Casiraghi -- which happened years before her first marriage (to Philippe Junot) was finally annulled by the Vatican. By then, it was too late to validate the couple's marriage in the Catholic Church, since he had died two years previously. But it didn't matter: all three of their children were born in line to the Monegasque throne, since the parents were legally married (Prince Rainier III having given his consent).
The separation of church and state is a universal reality in Europe, where religious weddings are conducted exclusively for spiritual reasons. They carry no legal weight, and are not necessary for marriages to be dynastic in any of the reigning monarchies -- which are largely secular institutions.
The 1999 nuptial mass celebrating the marriage of the present king and queen of the Belgians was purely a matter of personal choice: the fact that there was no impediment to a religious wedding in the Catholic Church was irrelevant. Philippe and Mathilde would have been legally wed, and their union dynastic (with their children born with succession rights) even if they had undergone only a civil wedding.
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