He started with an overview of what Shakespeare means to "the man in the street", which includes the idea of him as somehow timeless with something to say to anyone regardless of race, creed, social status, gender etc. He then took a fairly lengthy digression through the Marxist theories of Louis Althusser, with several lengthy quotes in quite technical language (perhaps technical in a Marxist specific sense, perhaps technical in a more general philosophy sense, I don't know). Eventually he returned to the point, which was the impact of these ideas on literary criticism, and how this ideology of a person as the product solely of their culture and upbringing was brought to the academic discussion about Shakespeare. Essentially the pervailing view in academia became that Shakespeare cannot be understood outside of his specific historical & cultural context, and that he's as sexist, racist etc as any other product of that background. And that the only reason he's regarded as some sort of universal genius is because we've all been indoctrinated during our schooling to believe this.
He then moved on to his own opinion on the subject - which is that while this backlash against the idea of Shakespeare as universal was necessary it has gone too far. He very briefly discussed the scientific work that lead him to this opinion - mentioning Richard Dawkins & Stephen Pinker. The idea here being that while we're products of our culture, there are also fundamentals that are common across all cultures. In Pinker's work this is language in particular, but also other things like emotions like jealousy, fear, love etc. (As an aside, although he didn't mention it in the lecture this is the Nature vs. Nurture debate - and the idea that it's one or the other is generally regarded as a false duality nowadays.) So his opinion is that there are things about Shakespeare's plays that speak across the generations and across cultures, but there are things that are the product of his time and place. He then said he didn't have time for many examples, but gave a few brief instances that demonstrated that Shakespeare was set apart from others of his contemporaries in how he wrote his plays. Shakespeare doesn't often take sides among the characters of his plays - people are rarely completely evil, even the villains are given redeeming features and given human motivations. There are also not the moralising introductions or epilogues that others of his contemporaries would insert where the "lesson" of the play was spelt out. So whilst Shakespeare might well've been just as sexist etc as the rest of his culture, the way he wrote his plays allows one to sympathise with the characters even when our modern perspectives are different to Shakespeare's.
Whilst he was quite a good speaker (although not good at reading out long passages from other's works without stumbling) the subject of his talk wasn't quite what the title and description of it in the booklet for the evening had lead one to believe. And I think the overall structure could've done with some reorganisation or tweaking for the audience - in particular I would personally have cut the lengthy discussion of Althusser's philosophy and presented it more briefly & in a manner that was more clearly related to his point, like he did with the biology later in the talk. And then have had more time to go into a few specific examples, perhaps contrasting different critiques of the same passage from the three perspectives so that we could see as non-academics what the practical outcome of this theorising is. I wouldn't've gone so far as to walk out of the talk (bad manners, if nothing else), but I did have some sympathy with the point of view of the person who did get up and grumpily announce "I thought this was supposed to be about Shakespeare" and leave, slamming the door behind him.