If an East India Company officer of sufficiently noble birth married an Indian Princess a couple generations earlier, their child married another white of high birth, and the son of that union became a prince of an important state, and was raised Anglican and remained so, I could see it.
This is almost plausible.
We should bear in mind that among the Spanish aristocracy, a large number of families have the blood of the royal Aztecs flowing through their veins, while certain British aristocratic families have African blood coming from Alexander Pushkin. The Earl of Liverpool, who served as Prime Minister in Victoria's lifetime, had Indian ancestry, and our own royal family most likely has Moorish, however diluted (not mentioning Charlotte-Sophia's supposed black blood).
So it isn't impossible to get Victoria to marry someone with non-European
ancestors: if they looked white enough, and said ancestry was remote enough, it simply wouldn't have been a major issue. The idea that you can pair Vicky off with Cetshwayo or one of the Ottoman sultans is, however, wayyyyyy out of the question.
It's interesting to suppose, though: imagining that the queen married someone of comparative ethnic background to the Earl of Liverpool - say, one-sixteenth Indian. We'll make this person the prince of a minor German state whose ancestors in the fifth generation include a high ranking BEIC officer who paired off with a princess of the Mughal royal family.
This is enough non-white ancestry for it to be
noted, compounded with enough social status or strategic importance for it to be
disregarded as a salient factor in the Queen's choice of spouse.
Suddenly, the concept of racial heirarchy becomes much more difficult to justify among the emergent eugenics movement.
"Well, the king is an Indian!" retort early critics of racial ideologies: a retort which, in a severely class-driven society is pretty powerful. The early eugenics movement has to undertake a complete rethink of the concepts of racial heirarchy and purity. Maybe Indians get re-classified as much closer to Europeans, if not equal. It would be the same sort of scenario which saw re-writing of the 'one-drop' laws of Virginia to accommodate the powerful, aristocratic descendants of Pochahantas who might otherwise have found themselves herded onto reservations.
Possibly, if the fact is not hidden, all things Indian will find a new degree of social acceptability. In future generations, the royal family might end up stressing it's aristocratic Indian descent (however remote) as a
legitimising factor in the continued governance of India.
Alternatively, the now-Prince Consort's ancestry will be hushed up and simply not spoken about.