I like stories, they are wonderful at illustrating concepts. To that end, I beg your indulgence, Tush, while I relate one that is here relevant.
My dog hates getting her toenails trimmed. She used to tolerate it better than she does now, and the worsening is largely my fault. When she gets her nails trimmed, I used to try to comfort her during the process, to reduce her fear. Unfortunately, my comforts became associated with the unpleasantness of trimming her nails, and now if I try to comfort her during this, it only makes her fear worse. In some ways, comforting her was an indication that there was indeed something to fear. I recognized my error and have subsequently adjusted my behavior. My dog still hates getting her nails trimmed, but she isn’t so terrified as when I tried to calm her fears.
How does this relate? People can be the same way. Our efforts to reduce the fears of others can have the opposite effect of the one intended. By trying to reassure “Men’s Right Activists” that we have no desire or intention of turning the XY persuasion into a secondary class of citizens, we may be confirming to them that their fears of such a situation are valid, and thus in turn we reinforce them.
The solution, then, may be to do nothing about them. Instead, we must focus on ourselves being clear in our actions and intentions, and ensuring that our actions are impeccable. If telling someone “there is nothing to fear” causes them to fear more greatly, then showing them that there is nothing to fear is a legitimate option to try. I cannot guarantee brilliant success -- by dog is still afraid of getting her nails trimmed -- but it might help things not be as bad.