Punks didn't exactly reject synths and certainly not on grounds of 'authenticity'. Suicide were a notable punk band who used them, while Magazine and Joy Division were big synth users and barely post punk. The reason they weren't emblematic with the first wave of punk was entirely down to cost - they were seen as a millionaire's instrument and therefore tasteless and decadent. Once Roland started mass producing, synths became far more popular with post punk bands and spawned an entire movement, from Cabaret Voltaire to Depeche Mode.
As I said, it was on grounds of general inaccessibility, not inauthenticity - the point was to make far more thrilling and relevant music by abandoning the overwraught playing, equipment, and production which had become the norm from the mid 70s. At that point, synthesizers were largely associated with millionaires noodling away in expensive studios and not part of the equation for a bunch of teenagers starting a band. The minute these bands started doing albums and synths started getting mass produced by Japanese firms, they began to pop up in the music from about 1978, just a year after the first crop of UK punk albums.
