It seems that MIT-Scheme needs the cc function to be a function of 1 argument (the return value for the continuation)[0]

Changing it to the following should work:

  (let ((start #f))
    (if (not start)
      (call/cc (lambda (cc)
                 (set! start cc))))
  
    (display "Going to invoke (start)\n")
    
    (start #f))

[0] https://www.gnu.org/software/mit-scheme/documentation/stable...