I think it is not good behavior & reflects badly on H to be writing hate mail out of the blue. But I think like the nuclear no-first strike policy of the Indian state is a good guide: if the indologist/ activist is the 1st to strike on H then the retaliation should be in kind though ideally not by sending them hate mail unless they sent a particular H hate mail first.
Instead the response should be in an appropriate (may be public) forum. Now as practitioners of dharma it is good to observe some rules of engagement in such encounters. If they have interpreted something in a way that you don’t like but are relatively firm ground doing so then there is no need for aggression at all. At best one can present their alternative interpretation. If they have made fallacious claims, presented false translations or false datings: expose those pointedly if interested but it can stop there without getting personal.
However, if the said indologist indulges in H hatred (covert or overt), political activism against H power & H dominance in the Indian state or meddles in internal affairs of H with the aim of helping enemies of H or abrahamistic potentates then all bets are off. So the rule of the thumb is any attack on H political power should be mercilessly countered by all available means.
I’ve interacted with some occidental indologists. Few were rude - reflective of their attitude to their objects of study. But some of them, even if they come across on the internet as anti-Hindu, were actual good persons as far as I could judge. I felt they should be spared hate mail & left alone. We have difference of opinion and our world views and politics don’t match in the least. However, the latter were not intrinsically wicked. We just let each other be in a state of non-enimity acknowledging our profound differences. That is consonant with H live and let live and also doesn’t push them farther towards anti-H positions.
Again a rule of the thumb is those with any subterranean abe’istic sympathies are more likely to be anti H than those who seriously outgrown abe’s ways.