A lot of ink and emotion have gone into this topic.  Argue away about the sonnets, everyone. Or the role of Antonio in "Twelfth Night,"  also Antonio in "The Merchant of Venice." 

During the English Renaissance men were, in general, more cultivated and educated than women.  Men went to University, for example, though Shakespeare did not. Nor did he need to, having gotten a great preparatory education in his grammar school.  Any education women got, however, had to be private.   This weighting of education in favor of men created an audience for brilliance that was comprised primarily of men. Men writing for men.

Queen Elizabeth I, of course, had gotten a stunning education. She amazed continental ambassadors with her capacity to discuss politics with them in Latin. But, ah, how many women had the Queen's advantages?  In my plays, I show Emilia Lanyer, the putative Dark Lady of the Sonnets, as a well-educated woman, having been trained by an extraordinary father to be an ornament to the Royal Court. 

But men were the wits, the poets, the playwrights.  When Shakespeare wrote his sonnets to the beautiful young man, he was writing, I believe, for money. And prestige. And reputation. Perhaps he was trawling for additional patrons. For years before their publication, manuscript copies of the sonnets were being passed around within the circles of young aristocrats. But perhaps Shakespeare was also writing with his heart.  I believe he had a crush.  And why not?  The Earl of Southampton was beautiful and aristocratic, with a great taste in literature.  He appreciated Shakespeare's work and was a willing and generous patron.  It is thought that "Venus and Adonis," dedicated to Southampton, was written at the Earl's estate, where Shakespeare was given  refuge from the plague sweeping through London, which it did with alarming persistence, repeatedly.  The playhouses were shut down, and a writer would be very grateful to find a bolt hole where he was fed and housed while he generated  income with a long erotic poem.  The erotic poem is heterosexual. Why not? On the other hand, it does focus on the dazzling loveliness of the young Adonis which has driven Venus mad with desire.

There is evidence that Christopher Marlowe was homosexual.  But Shakespeare?  I think the argument there is thin.  One is required to extrapolate so much from the writing, when Shakespeare is famous for trying out viewpoints and being impossible to pin down as to his "own" viewpoint.  He savors all of humanity.  What does he endorse, apart from basic decency?

In the third play of my trilogy, "'Twas Ever Thus: Betrayal,"  I intend to portray men fascinated by other men.  I have been cautioned, "Now don't make this your gay play!"  Why not? I wonder.  Well, first of all, I never want a play of mine to be simplistically defined in any way.  Secondly, I don't want to show something that may not have been true at all. And, thirdly, I find a sweetness and wistfulness in the concept of a crush.  Is it possible that a crush can be more powerful and more deadly than True Love?