Shakespeare had a wife and family. He wrote a lot of plays celebrating heterosexual love. Some of his Sonnets - which may or may not be autobiographical - are addressed to a woman - the so-called 'dark lady' with whom the writer clearly had an adulterous sexual relationship. The idea that he may have had a similar relationship with a young man comes from the other Sonnets, which express intense but idealized affection for a 'lovely boy'. Though there is nothing explicitly sexual about this relationship a number of critics, especially but not only in recent years, have argued that it is sexual nevertheless. So there is no simple answer to the question.