There were protesters every once in a while at the DC in my years growing up, but not at the CA/SAD. Anytime protesters/picketers were there, everyone just avoided them, then laughed at them once safely inside. It definitely reinforced the Org's message that "apostates are mentally diseased."
Someone more qualified than myself can probably give you some explanations around cult/high-control-group reflex reactions, even among those who have doubts about doctrine/rules.
I'm not sure if members' reactions would be different if it was something as simple as a banner hanging nearby that read: www.jehovahs-witness.net (Maybe with a "'The Truth' is Out There..." Hahaha....) That way there's no person that can been seen as "crazy", no clear message that defines an issue you could be "bitter" about, just a website whose URL can be easily remembered.
If I saw that, I'd think "Hmmm...obviously 'apostate', but I wonder what that website is?" As much as humans are naturally defensive when their [faith] community is under attack, they're equally imbued with a natural sense of curiousity.