I believe these groups are aware that they are fighting for an action through rhetoric that use factual statements that can easily be shown to be incorrect. Further, it seems like they believe better facts supporting their view could be found if their actions were implemented because they insist so much that their subjective truth should be respected to the same degree as real facts that disagree with their subjective truth.
My interpretation is that the awareness of their factual problems is what motivated these groups to develop a pattern of violent intolerance towards anyone that questions it, as people that do not agree with the action would otherwise outnumber them in the discourse and make it harder to implement the action.
There seem to be a synergy between alt-right and social justice warriors in particular, as both narratives need an antagonistic other that justifies why it is ok to be violently intolerant towards anyone that questions their view.