The sad truth- this was a royal family that was never deeply embraced by the majority of Greeks. I think of the Greek royals as a failed transplant: Some roots grew and indeed took hold for a while, but they were neither strong nor enduring. To me, Frederike's negative impact on the wobbly Greek monarchy was as catastrophic as that of Alexandra Feodorovna on the wobbly Russian monarchy.
I don´t quite agree on this; having watched 100s of old greek movietones from the 1950s and 60s I know how poular both Paul and Frederica were - even more than Kings and Queens of other monarchies whose thrones still exist today.
Paul, but Queen Frederica even more so, have been tremendously hands-on, open and embracing people and when I see them interacting, I sometimes can hardly believe that this was a royal couple in the 1950s, where many other Royals very much kept their distance from "the people". In these old films you can easily see how much the greek King and Queen were cheered and mobbed wherever they went - not even at big splashing occasions, but also average engagements where many 100s of people were waiting eagerly to see the royal couple on normal working days.
When the King died, thousands of people were mourning him, waiting for hours to pass his coffin, lying in state. Some women fainted when the funeral procession passed by.
One must not forget that the greek monarchy was never driven out of the country, especially not under King Paul and Queen Frederica, but had to endure a coup while a young, unexperienced King in office tried to do something about it after he had sacked a very popular old PM against the majority in the greek parliament, and then decided to leave with his family himself. Constantine was not a reluctant Nicolas II. And his mother didn´t really play an influential part when he and Anne-Marie were on the throne - even though anti-monarchist propaganda would wanted to make people believe that. And that narrative still works today! The truth is, that Queen Mother Frederica pretty much retired from many activities (of course, she kept on doing royal engagements like visiting sporting events or opening new clinic wards etc.), after in the mid-1960s criticism appeared about her alleged influence on the monarchy.
And no - Queen Frederica is hardly comperable with the russian Tsarina! These 2 women had very different personalities! The one lady was totally overstrain in many ways of her role as wife of the emperor and as a mother, obviously living somewhere among the clouds, while the other one never lost her feet from the ground and has done a lot of good for the improvement of the life of many greek people.
I think there might be many reasons why F. became unpopular. Attacking the consort, especially when it was a woman, and you are not daring to rival the King in charge, is nothing new. King Paul always made his own decisions and his wife was both political as well as in private his substitute (there was also a big age gap between them) and it is known today that the Queen always looked up to her husband!
Then, Queen Frederica was born a german, which was also nothing that was helpful or would speak for her in the eyes of those opposed against the idea of monarchy. Still, she was popular with many greek people in the countryside. There also was a diffence between the average people in provincial Greece and some parts of the political elite in Athens, who accepted the monarchy because they really couldn´t do something about it, rather than supporting it.
And the most unjust thing about this story is that in 1964 who proposed to G. Papandreou to legalize the communist party, it was King Constantine , and G.Papandreou said NO to legalization. 
