After giving it some thought, and a good night's sleep, I have made some changes to my attitude towards Shakespeare. I realize now that he is a product of his time and culture. But by taking the words of his plays and setting them in modern times, it takes them out of his time and culture, and for me, makes them less relevant, not more. I can handle his antiquated notions about women or mental illness if it's set in the proper place and time. Seeing it in today's world just drives me crazy. What's so wrong with people watching the words set in the time and culture they were meant for? Why can't people just imagine life back then instead of having things redone for their time? Maybe that's why I've put off watching Ten Things I Hate About You for so long...??
The other issue is the language. It's tough, but I realized that for myself, it's easier to think of it as literally a completely different language than English. The words might be words I know now, but they aren't what they were then, and that makes them completely separate from today's language. So, it does need translation, and studying and all that to really get it.
I realize now I was reacting to seeing Shakespeare set in modern times. I have never had a problem watching or listening to or reading the old-school stuff. I really think that's the key that's getting go me.