Al Sharpton, Noam Chomsky (a lot of the time), Ted Kennedy (60% of the time),Paul Foot, Dennis Skinner like to think of themselves as popular members of the left.
Most right-wingers tend to identify the left with them.
Most of us on the left actuall reject their message, something those on the right fail to comprehend.

("A liberal does have the philosophy of using armed force to remake society in his image". Sorry, was that a direct quote from Rush?)

Right extremists are a bunch of loons too.........
Ralph Reed, Pat Robertson, Jesse Helms, Trent Lott (lots of the time), Margaret Thatcher, Norman Tebbitt ..............
Repeat as above except switch left for right where appropriate.

For specific points in your post:
Chomsky throws a lot more weight around the "official" left movement than Falwell does on the right.

See list of names above. Radical conservatives are behind many of the GOP PACs - gee wonder who helps to control the agenda there?

What Chomsky says is taken as gospel by these people, and incorporated into the left-wing culture in this country.

These people as in all us liberals? Well, either tar us all the same or dont. Sheesh, no wonder Mary Anne left.
As far as I am concerned, Chomsky should stick to language - he made more sense then. He advocates anarchy (probably an anarcho-syndicalist collective, but that would be too funny) and believe it or not, you wont find many people of any persuasion agreeing with him.

It has been my thesis that most Democratic voters, minorities, labor union members, and people who consider themselves "liberal" have overlooked--either deliberately or unconciously--the fact that the formal left-wing movement in this country has gone completely around the bend, and that the national Democratic Party is close on their tail

Substitute Republican, left etc and you'll get what many similarly blinkered liberals/leftists see.

Cheers,
Tony