I know this answer is a little after you posted but I was going through the sub and thought to address this. I’ve actually never heard this claim and I’m curious to where it comes from.

There is no evidence to support the claim Shakespeare was black.

We don’t have a great surplus of information about Shakespeare‘s entire biography. There is a period called ‘the lost years’ between 1585-1592 where we don’t know exactly what he was up to. This isn’t a conspiracy to erase information about him, but rather endemic of the record keeping of the time. Very few written records of ‘common’ people existed. There would be a line in the church registry when he was baptized, married, and his children were baptized. Legal documents such as wills, school records, and court cases would also be what is left behind. After 1592 Shakespeare started acting and having his plays performed in London and then we have many records of flyers for his plays and the publications themselves. No where do we have any mention he was black. We do have journals of other people in London describing his acting and writing and they certainly would have mentioned this about him.

We do have two certain portraits of Shakespeare but they were done in the first few years after his death. He has a funerary bust here above his grave that is painted and he is white on it. The monument has gone through phases of restorations and painting itself but original descriptions of it show it to have light skin. However it was made after his death to adorn his grave. The Droeshot engraving here used for the First Folio collection of his works was published in 1623 and he died in 1616. The Chandos Portrait here was painted before 1610 and Shakespeare died in 1616 on his birthday. He is certainly fair skinned in it when considering the age of the painting and lack of restoration. Time and candle smoke and exposure to light will darken it significantly over time. We cannot say for certain it is Shakespeare though the National Portrait Gallery holds it is after much research.

There were black Elizabethans in England that held various degrees of prosperity and integration which is described in a book I’ll link below. Shakespeare did write one character, Othello, who was a moor from where we would consider Northern Africa or black by our current acceptance of how to define that. Much scholarship has been devoted to race in Shakespeare for further reading. I think it would be interesting if he had been black, but there’s not evidence out there to support that claim.

Sources For a great biography check out Stephen Greenblatt’s Will in the World. Shakespeare, William, and David M. Bevington. The Complete Works of Shakespeare. New York: Longman, 1997. Print. Bloom, H. (1998). Shakespeare: the invention of the human.

To learn about being black in the 16th century read this great book Black Tudors by Kaufman