Sherlock Holmes observes that it is a capital mistake to theorize in the absence of data. There is very little data here, so any theories will be somewhat precarious, but let us start with Washington's own words from the opening chapter of Up from Slavery:

Of my father I know even less than of my mother. I do not even know his name. I have heard reports to the effect that he was a white man who lived on one of the near-by plantations. Whoever he was, I never heard of his taking the least interest in me or providing in any way for my rearing. But I do not find especial fault with him. He was simply another unfortunate victim of the institution which the Nation unhappily had engrafted upon it at that time.

Washington himself did not know who his father was. He had merely heard rumors. Assuming those rumors to be correct, he still had no reason to feel the slightest affection for or obligation to a man who did nothing whatsoever for him. It therefore seems to me that there is no good reason to suppose that Washington's racial attitudes had anything to do with his parentage.

If we look for other explanations for Washington's accommodationist attitude, however, there are some fairly obvious ones. Washington owed his early education to the Hampton Institute, a collaboration with white people of precisely the kind he was to champion. It was Hampton's president, Samuel C. Armstrong who used his influence to have Washington appointed as head of the Tuskegee Institute, later Tuskegee University,at the age of twenty-five. Washington achieved early success through friendship and collaboration with white people.

Quite apart from this, Washington lived and worked in the South. What course other than accommodation was open to him? It is impossible to imagine him achieving anything like the same success as a Marcus Garvey style firebrand. Washington's public attitudes to race and racial collaboration make perfect sense without our having to hunt for reasons in his parentage.