How to respond to papers that put forward unreasonable criticisms of my research area?
You can't change what is already published, so there is no point in trying to.

What you (and the people in your research area) can do is ask yourself why they used A instead of X. Maybe there is an easy-to-use free implementation of A, while it takes a PhD to really understand and implement X properly? In that case, you and your peers should fix the problem by releasing a tool to do X. Possibly an automated one, with a simple interface and no magic parameters to tune. Then you can recommend it to people in the other field.

Another thing you can do is collaborating with someone in that area, and publishing a benchmark paper where you test several algorithms and you show that X really works. A paper of this kind may be easier to publish in their area than in yours, where this fact is common knowledge.

If you simply call them idiots, you will never fix the problem. This is the wrong attitude; the blame can't be all on their side. You should borrow this principle from user interface research: if your users make mistakes frequently when interacting with your program/website, it is not their fault because they are idiots, but it is your fault because your interface is bad.