As shown above in #49, 5000 Russian aristocrats, officers, and soldiers showed up when Vladimir was proclaimed heir in Paris in 1938. The recent letter is just from 4 aristocratic supporters of Dimitri Romanov and not even backed by the Romanov Family Association either.
While Nicholas II was against Vladimir's parents marriage he had changed his mind and that marriage had royal support long before Vladimir was born. Even Vladimir's marriage to Leonida did not cause a revolt in support from Nicholas, his brother and others.
It was on his death that Dimitri and his brother Nicholas came forth as claimants. They felt the rules about morgantic marriage didn't applied to them as Princes just to Grand Dukes and it was then they questioned Maria's parents legitimacy. This is something the Russians are also fully aware off as Vladimir had visit Russia as the unquestioned pretender before his death.
Also Dimitri does not have the support of all descendants outside of the Kirill branch with Maria having the support of the Kirill branch. Karl Emerich Leiningen from the Kirill branch is also a claimant as is Rostislav a descendant of Michael/Xenia (although he is somewhat in union with Dimitri). There are even some outside the family suggesting Prince Michael of Kent or even Prince Harry as an alternative. However, many descendants seem to be not backing anyone. Even the Romanov Family Association, while it rejects Maria, officially don't back Dimitri but leave it up to the will of the Russian people.
As for the Nazi accusations: First off even if relatives had supported the Nazis that is not a reason to deny Maria's claim as it has never been a reason to deny any other royals' claims. Also they are misstating the facts he was not a supporter of the Nazis but a prisoner as were his sisters.
As shown above in #49, he rebuffed the Russians and being made Regent of Ukraine. In 1942, while living in France he was captured and put in a concentration camp at Compiègne after he refused to issue a manifesto calling on Russian emigres to support Nazi Germany's war against the Soviet Union. In 1944 the German army moved the family inland and eventually to his sister Maria's in Germany. They were not free, they were not supporters of the Nazis. Maria's husband was forced to join the army, captured, and died in a Russian concentration camp.
His sister Kira and her husband Louis Ferdinand of Prussia worked with the underground and were captured and thrown in Dachau Concentration Camp. They were rescued by American soldiers at the end of the war. His future wife Leonida's first husband Sumner Kirby died in hospital near the concentration camp he was put in.
https://en.wikipedia.org/wiki/Grand_Duke_Vladimir_Kirillovich_of_Russia
https://en.wikipedia.org/wiki/Grand_Duchess_Kira_Kirillovna_of_Russia
https://en.wikipedia.org/wiki/Princess_Leonida_Bagration_of_Mukhrani
The Romanoff Family Association
