It was WIlhelmina herself who later in life came to the conclusion that a marriage to Dutch commoners would be best - somehow to be 'one with the people'. She writes about this in her autobiography. She even preferred a non-noble as it may otherwise lead to petty squables between aristocratic families. This thought was supposedly shared by Juliana and Margriet.
Claus was from the lower aristocracy - his grandfather was the head forester at the court of Mecklenburg. In that light I never understood Beatrix thinking Pieter's background, from a very decent patrician family- was so much worse. The Van Vollenhovens delivered a mayor of Rotterdam, a mayor of Amsterdam, several members of parlament and the diplomat Maurits van Vollenhoven married a Spanish Bourbon (daughter of the duke of Durcal). Prof. Cornelius van Vollenhoven taught Juliana at the University of Leiden. Some added other last names to theirs or acquired a Lordship. The Von Amsbergs owned a few farms in Mecklenburg and were only ennobled not that long before.
Also Princess Armgard, the mother of Bernhard, was against the marriage to a commoner. While she herself lived with a Russian refugee colonel Pantchoulidzew for decades and was married morganatically to Bernhards father.
But apart from him not being noble there were other factors making it easier to sideline Pieter. First of all he was Dutch. And that made it much easier for people at court but also in the country to measure him up, to place his accent, his family etc. And compared to the nobles working at the court, he/his family was indeed of lower social status. And secondly while Claus was a diplomat, a gentleman moving in the higher social circles (a friend of Prince Richard of Berleburg and Beatrix and Claus met at a party organised by Beatrix cousin count Oeynhausen) and married into the family when he was around 40 and with a career, this was not the case for Pieter. Pieter was less 'presentable': young, green, 'a typical student from Leiden with too much bravado to hide his insecurity' said Biesheuvel. He came fresh from university, had no carreer yet.
They simply didn't know what to do with him. And at court I don't know if they ever warmed up to him. And this dislike was brought over to his sons, all of which were considered a bit 'too light'. The press interest in Maurits and Marilene [he was the first one to get married] was a source of irritation in the Hague. Pss Margarita in her infamous interviews with her first husband also confirmed that impression. I was in the Museum van Loon - the canal house of Mrs Martine van Loon-Labouchere, by then still grand mistress of the court- on a visit a long time ago where a tourguide started ranting about having a princess named 'Anita' (a name sometimes indicating a lower social status, even though her family is perfectly respectable).
I remember a documentary about Beatrix where a lady-in-waiting was praising the good manners of Beatrix' sons while referring to *some* popular others who didn't bother to shake her hand at a new year´s reception. From the context it was clear she meant Maurits and Marilene. I don't disagree completely: we don't need to see princes behind DJ tables and I do find these people from Amsterdam heading to Ibiza not very chique either, but what does it matter? And now the most vulgar of all of them is the granddaughter of the very posh Beatrix and the even posher Laurens-Jan Brinkhorst, -not a Van Vollenhoven- which is a great joke.
The only working class person married into the RF is Annete Sekreve, and she seems to have done so with ease. All the others are indeed upper middle class or in the case of the Brenninkmeijers: upper class. Personally I would expect a hypothetical Daniel Westling II marrying the heiress would be popular but he could also count on a lifetime of petty and snide remarks about accent, lack of university degree etc.
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I am going through the biography of Foreign minister -and later NATO secretary general- Joseph Luns, himself married to a baroness van Heemstra. It says that in 1964 Prime Minister Marijnen told him that Juliana had informed him that 'Margriet regarded herself as engaged to the law-student from Leiden, PvV'. Marijnen thought that such a 'morganatic marriage' would be a danger to the monarchy and such children would not be accepted as heirs to the throne in the case of Beatrix being unable to have children. Luns -of course- agreed completely, though he also anticipated that parlament 'from a wrongly interperted egalitarian-principle' would approve of such a marriage, but that this would not prevent 'a later negative attitude of the Dutch population'. Luns urgently advised Marijnen to convice the young man to retreat for the sake of the royal house. He recruited the help of former minister Beerman (like the Van Vollenhovens also from a patrician family from/near Rotterdam) to convince the parents to end this 'completely undesirable idylle'.
Earlier Luns had complained to Bernhard himself that Queen and prince acted completely unprofessionally in finding a partner for their eldest daughter. Beatrix socialising with 'enthusiastic and idealistic young people with all sorts of progessive plans and with quastionable backgrounds and long hair' did not help and Beatrix needed to get in touch with foreigners of equal standing (he used the German 'ebenbürtig'). Note that the group included Laurens-Jan Brinkhorst, Laurentien's father. In the mean time he talked to cardinal Alfrink how the Vatican would regard a catholic marriage where the children would be raised as protestants - in case that like her sister, Beatrix would meet a catholic Prince.
Luns advised Bernhard to make a list of candidates between 28 and 37, starting in the UK. He suggested via ambassador Van Rooijen -also well known at the court) to approach the private secretary of Queen Elizabeth II. The prince agreed, Van Rooijen started working and early 1965 several dinners were organised. This was not a success, Beatrix though the English were 'too aloof and cold'. At a dinner in Germany she would later meet Claus, who was invited to make up numbers, and who was not supposed to be the one that would actually be chosen over more high ranking candidates [including Prince Richard of Berleburg]. Beatrix herself said that she had met Claus already before this dinner party [at another one] and was already in love with him.
Note that in her Beatrix biography Jutta Chorus says that Juliana advised her daughter in 1962 already to look for a partner ´in Anglo-Saxon circles´, so the Luns biography may have some dates wrong. Huub Oosterhuis [family friend] said: 'she didn't like that at all, those cold English, that distant and closed British aristocracy. She thought Germans were warmer, more European and closerby' [I assume he meant mental proximity]. Although Margriet is not referred to in the book, Chorus points out that Beatrix was simply madly in love, which perhaps made her overlook some objections she may have had earlier for her sister.
Luns was also against Claus: low nobility and -faulty- enquiries told him that Claus was 'a typical snob, arrogant, vain and chasing women'. Supposedly he had had a relationship 'with the much older and mundaine comtesse de Riberg and at the moment with a secretary of the Swedish embassy'. Luns realised his point-of-view was not modern but he maintained that for the Dutch population 'any prince would be better than the best count. And any count would be better than the best baron etc'. He was very irritated that the ministers had 'weak backbones' and bowed to the 'not very dynastic preferences of Queen Juliana'. Supposedly Beatrix loathed Luns for the rest of his life, he was never made a minister of State, while he would have been the most obvious candidate for such a position.