I do think Prince Luitpold and Tsarvitch Alexei could be twins. How closely were they related? Because all European royals had some blood in common.
They were not closely related, but both had Hesse(-Darmstadt), Württemberg, Mecklenburg-Strelitz etc. blood. Some ancestors they shared:
- Karl II. Duke of Mecklenburg-Strelitz (1741-1816), father of Queen Luise of Prussia (Alexei´s great-great-greatgrandmother) and of Duchess Charlotte of Saxe-Altenburg (Luitpold´s great-great-greatgrandmother)
- Friedrich II. Eugen of Württemberg (1732-1796), both Luitpold and Alexei´s great-great-great-greatgrandfather, as he was the father of Maria Feodorovna, Tsar Paul I.´s wife and of Duke Ludwig of Württemberg
So Alexei and Luitpold are "cousins".