For the greater part of the 20th century, acting stemmed from Stanislavski. You can go back to Meisner, Adler, Strasberg, Hagen, or anyone else that was a major force in teaching acting, and they will tell you that it's basically stemming from Stanislavski. He was the first person to state what psychological realism was and how to get there. Most people never learn a pure "Stanislavski" technique, but they learn different ways and emphases of what he taught. That foundation has shaped acting for the 20th century. Now, we wouldn't accept anything different.
By the way, Shakespeare isn't a method of acting. He's just a genius. Gosh.
Some people paint, some people sew, I meddle.