Modern Leftism/Progressivism actually has little in common with Bolshevism except for one thing: neither ideology will tolerate the presence of any line of thought other than its own.
The Bolshevists believed it was their mandate to create a classless utopia, and to mow down anyone who stood in their way.
Modern Progressivists are more about social engineering than they are about classless utopia. Their vision more closely resembles something like Aldous Huxley's Brave New World. They have taken control of our schools and universities in the hopes of reducing (and eventually rendering extinct) those who would oppose their dreams of eternal cappuccinos and orgies.
The face of modern Progressivism can be deceivingly warm and pretty at times. But peel it away and you'll find something even Stalin might balk at.
The Communists never wanted a classless society. They simply wanted to make the decisions as to who was in what class, e.g., themselves at the top with all the power, everyone else having none. Exactly like the "progressives" today.