It's not a duty or responsibility. And it's not unproductive as a sibling commenter suggests. It's straight up counterproductive and a form of self-sabotage.
If your goal is to feel self-righteous and superior, by all means attack those who are showing genuine interest in coming over to your side. If your goal is to actually bring about a positive change in society, perhaps it's worthwhile to consider a different approach.
This is based on an almost ludicrously simplistic straw man: you conjure up the idea of someone who is "showing genuine interest in coming over you your side"
How are they 'showing' this exactly?
What makes it 'genuine' that they want to come over to another side?
Why are they on a 'side' in the first place, and what makes you think that the goal is to have them change 'sides'?
Are you saying they are not already on 'our side'? What does that imply?
How can you distinguish their arguments from those of people who simply want to argue their position and remain ignorant?
If your goal is to feel self-righteous and superior, by all means attack those who are showing genuine interest in coming over to your side. If your goal is to actually bring about a positive change in society, perhaps it's worthwhile to consider a different approach.