Wearing my professional historian’s hat, I’d have to say he wasn’t gay, because ‘gay’ wasn’t an identity in Shakespeare’s time. In the fifteenth and sixteenth centuries, there was an admiration for the beauty of women and for boys, in terms of androgyny. Christopher Marlowe wrote about it as well as Shakespeare, namely older men looking at younger people, which makes us incredibly uncomfortable today as it goes against our ways of looking at sexual desire. If you read a sixteenth century love poem to a lady, the writer was most probably sexually attracted to that lady, so the language that Shakespeare at that time meant he was showing an attraction to both women and boys: he’s not in the non-sexual realm of male-to-male social bonding, it’s clearly erotic desire.
"Interestingly, for most of history the queerness of Shakespeare was erased, because the sonnets were mostly published in altered editions"
So, in modern terms, you could say Shakespeare was bisexual with a bit of paedophilia stirred in, which was pretty normal and perfectly respectable in those days. When I say normal, there is an argument in medieval and Arabic society that the traditional pattern was for men to be attracted to women, and to boys, but not to other adult men, but then when the boy hits puberty, and starts growing a beard, the man loses interest in the boy.
Rufus Wainwright performs Sonnet 20, which contains ambiguous references to beauty
It was the same in Ancient Greece and Rome. But that pattern changed in the eighteenth century, when same-sex desire was thought to be wrong in all forms. I think it really does matter whether Shakespeare was gay or not, because he is used as a yardstick of the value of English culture, so it makes a huge difference if you can say that the greatest writer in the English language is actually not classified as ‘normal’. Interestingly, for most of history, the queerness of Shakespeare was erased, because the sonnets were mostly published in altered editions. It was only later, in the nineteenth century, that people discovered that they weren’t reading the original texts, when they went back to the original text.
It does matter to know if the writer of Shakespeare was gay as it gives a better understanding of the writer and his background. What is known about Shakespeare, and very little is including whether or not he could even write, is that to all intents he was a married heterosexual family man. However the other man most likely thought to have written the Shakespeare plays - Francis Bacon - who deliberately disguised his own identity to conceal his own royal birth, was a known bisexual in his own life time and was extremely close to Henry Wriotheseley, the beautiful 20 yr old who is the major suspect as the subject of the love poems in the Sonnets attributed to Shakespeare. This fact lends more proof to the version of events that it was Bacon who wrote in the masked name of Shakespeare. see www.theroyalsecret.info on the extraordinary life and loves of Francis Bacon and my book The Royal Secret published in 2016 on Amazon.