Answer

Hello Dan.
The problem is familiar. In my experience, the most fanatical and least willing-to-listen group is the church of atheists. If you were to raise heretical arguments in the study hall of Satmar Hasidim, and certainly in the Ponevezh yeshiva, they would listen to you much more. Someone who doesn’t listen will not listen to what you say, and so it seems you will fail with him.
Still, there is value in responding substantively in such a place, because on every such site there are also many passive readers, and if you present arguments there is a chance they will read them too. One has to know that in most cases the passive readers are far more numerous than those who comment, and therefore the impression created by the comments does not in any way represent the value and benefit of what you say. But it is worth examining carefully whether you are in fact responding correctly, at least with respect to those sites. You need to know the arguments and the language, and you need to be careful about stock slogans common in the religious world. That is not the right way to address people there, and it will only arouse more contempt and mockery.
Beyond that, it seems to me that it is important to write this itself on the site, again for the benefit of the passive readers. Explain that people there mock instead of engaging substantively, and that it is hard to conduct a discussion that way (incidentally, that is why many people do not join in, and the discussion is lacking. They can go on delighting in themselves when no one else expresses different views, but that is not really a discussion, only blowing off steam). You can also add that in many cases the mockery comes to cover up the lack of ability to answer and engage substantively. The participants themselves probably will not listen to you, but others may benefit from it.