How would you argue that Twelfth Night is still relevant today by using themes?
One way of approaching this question would be to consider how you would stage a production of this excellent play if you were a director, and how you would highlight the themes that you feel are relevant to society today. One of the themes that we can definitely relate to today, given the current financial crisis and the cult of personality that is so important is that of the dangers of ambition.
Clearly, any discussion of this theme would have to focus on the character of Malvolio, who we discover has massive ambitions to rise above his station. Of course his ambition makes him a sitting target for Maria, whose letter wonderfully manipulates his hopes to convince him that his mistress is in love with him, which is something that Sir Toby and other characters find so amusing due to the difficulties of achieving social mobility in Shakespeare's time. Consider the famous quote from the letter that Maria writes to Malvolio, pretending to be Olivia:
In my stars I am above thee, but be not afraid of greatness. Some are born great, some achieve greatness, and some have greatness thrust upon 'em.
The play is the story of how Malvolio tries to reach for greatness that is above him and falls terribly, to the great amusement of others. If we think about this theme of ambition and how it relates to the financial crisis, I think it is perfectly clear that using this theme the play is very relevant to today's society. Shakespeare produced plays with timeless themes, and this is one example of a theme that is equally applicable to today's world as it was in the world of Shakespeare.