One of the most nuanced and important challenges to the EC proposal has come from MOGiS e.V, a German organization of child-abuse survivors. They've issued a statement condemning the proposal on several grounds: first, that censorship is unlikely to attain its stated goals and will create new harms, and second (and most importantly), that the EC should be turning its attention to making it easier for EU member-states and other nations to actually shut down sites that host images depicting the abuse of children.
Christian Bahls, a spokesperson for the group, says, "Blocking just hides the problem and actually lowers the police's incentive to become active. Also, going after the servers means a small chance of catching the people that put it there in the first place. Images of child abuse are outlawed all over the world. There is a global consensus that this imagery is illegal and should not be distributed (see the 193 Interpol members or the 117 signatories to the 'Optional Protocol to the Convention on the Rights of the Child on the sale of children, child prostitution and child pornography')."
MOGiS e.V. was formed in Germany in 2009 in order to fight censorship proposals there, and now they are extending their work across the EU, along with other anti-censorship groups, to call for meaningful solutions to the abuse of children and to fight against unworkable, dangerous knee-jerk censorship proposals. Their slogan is "Remove, don't block! -- Act, and don't look away!"