My understanding from reading through hundreds of comments/tweets of THEIR reactions to #NotYourShield's reactions to Schafers joke is that they believe some combination of the following:

• NYS was started by sockpuppet accounts which is "proven" from some screenshots of a 4chan discussion
• Even if there are women/minorities/LGBT members of NYS, it is still comprised MOSTLY of sockpuppet accounts (I don't fully understand what this particular belief uses as a quantifier, actual accounts? individual tweets?)
• Some or all of the proof photos by NYS are fakes or photoshopped
• The minorities that do exist in NYS are being "manipulated by the Neo-Nazis at the center of Gamergate" (I'm not kidding, could have been a troll but I looked at that person's account history and it didn't seem like it)
• That Gamergate uses NYS to deflect criticism like saying "I'm not racist, I have a black friend." (Much like it was presented in that video by TGWTG which Sargon later slapped around like a silly fish)
• That the people of NYS are trying to speak for ALL of whatever group they are from (which in and of itself completely defines the Anti-NYS misunderstanding of NYS)
• That NYS is somehow illegitimate because of it's relation to Gamergate, or because of another reason on this list
• Some people feel hostility towards NYS for "accepting things the way they are", "ignoring the danger towards other women/minorities", have "internalized misogyny/racism/homophobia"

Basically they have created an argumentative shield wall that completely defeats any possibility of NYS existing or having a valid argument or right to exist. Basically they deny that the members of NYS any sort of intellectual self determination. I really do not know how to break through to some of these people, but as a minority myself I have to say that it was the Anti-NYS SJWs that made me break my neutrality and go NYS.