Do any modern ("free-thinking") monks or monastic orders discard elements of the Vinaya? Yesterday I spent some time studying one of the Vinayas and, completely honestly, I couldn't help but think that some of the rules were shockingly superstitious even by the standards of most of the world religions of the time.  For example, rules that emphasize non-violence to such an extent that they forbid monks and nuns from slicing or peeling their own fruits and vegetables.  The food, completely vegetarian, must be "slaughtered" by a lay donor before the monks are allowed to break it or bite it.

I couldn't help but think that such rules actually harm the Sangha by preventing them from operating in present-day capitalistic societies, where self-sufficiency is highly respected and prized.  (And, potentially unsanitary?  Modern churches, by contrast, issue each congregant a separate cup and communion wafer, even though the disciples shared a single loaf and chalice.)

Other parts of the vinaya were surprisingly in-tune with modern sensibilities of social justice and  "Twitter feminism", such as the rule forbidding monks from teaching nuns without being first asked.  #DontMansplainDharmma  Or the rule that a monk must first ask permission of another monk (trigger warning) before reminding him or politely asking him about a possible rule violation.

It made me wonder if there are modern monks and monastic orders that explicitly (and unapologetically) reject the obsolete parts of the vinaya while conscientiously obeying the beneficial parts.  Granted, which parts are obsolete is open to interpretation.

And secondly, I am aware that the text of the vinaya forbids monks from criticizing vinaya or requesting changes to it, especially for the cause of expediency or attracting new followers.  The Buddha himself authored vinaya and expected it to be followed.  Is it permissible for a Buddhist lay follower, one who has taken refuge and has chosen to follow the Eightfold Path without picking and choosing, to discuss certain aspects of the vinaya in a skeptical light, as I have just done?  Or to describe certain texts as mythological or historical disciples as impure?  I have not taken refuge in the Three Jewels and will not unless I can do so in total sincerity and a pure conscience.
CASE 16. UMMON'S SEVEN-FOLD ROBE
  
  Ummon said, "The world is vast and wide; why do you put on
  your seven-piece robe at the sound of the bell?"
  
  Mumon's Comment: When one meditates and studies Zen, one extinguishes
  the attachment to sound and color. Even though some have attained
  enlightenment by hearing a sound, or an awakening by seeing a color,
  these are ordinary matters. Those who intend to master Zen freely
  master sounds or colors, see clearly the nature of things and every
  activity of mind. Even though this is so, now tell me: Does the sound
  come to the ear, or does the ear go to the sound? But when both sound
  and silence are forgotten, what would you call this state? If you
  listen with your ear, it is hard to hear truly, but if you listen with
  your eye, then you begin to hear properly.
  
  If you are awakened, all things are one and the same, If you are
  not awakened, all things are varied and distinguished. If you are
  not awakened, all things are one and the same, If you are
  awakened, all things are varied and distinguished.


You're being way too literal.  The continued execution of religious prescriptions rarely has anything to do with the more or situation that first gave rise to it.  Tradition carries it forward, but not without it first establishing something far more interesting in the process.  Each training rule is an opportunity to subjugate the ego.  Whether it's a matter of how many bowls you own, how you wear your robe, or how you address members of the opposite sex, each instance bends the will away from one's personal concerns and toward the dharma.  In following these laws, we forgot ourselves.  That forgetting is what's important; most of the rules themselves are almost arbitrary (although let me be clear - some exist that are utterly mandatory).

There's a really great movie entitled Spring Summer Fall Winter and Spring.  If you get a chance to watch it, pay close attention to the doors.  Every doorway at the monastery depicted in the film can be walked around.  They are just doors built in empty space.  They don't take one through a gate or into a sealed off room.  In practice, there is absolutely no need to use any of them.  But all of the monks do (and poignantly, those who have gone astray do not).  Training rules are no different than the doors depicted in that film.  In fact, the rules are doors themselves.  Each one is an almost arbitrary limit that we place on ourselves.  Nevertheless, when we choose to take up these kinds of restrictions, they convey us into rooms we would not otherwise have been able to reach. 

Only when we carefully put on our seven piece robe can we pass through the door that leads to the throne room of the Buddhas.  What does it mean to put on that robe?