I suspect economists are often ignored because those who are in power understand that economics isn't as scientific or as rigorous as economists want people to think. One economist's model predicts that such and such will occur. Fine, but another economist's model says that something else will occur. The problem is that the models are untethered to reality by replicated, unambiguous experiments. So the choice of which economist to follow becomes a political act.
Governments barely listen even to climatologists because their models, too, are problematic. Sure, there's consensus, in this case, that global warming is occurring and that people are to blame. But the climate is fiendishly complicated, and models necessarily simplify. If you tweak one parameter in the model, the predictions change drastically. So politicians don't take that science as having ironclad predictions. Indeed, the predictions have already been off in terms of when irreversible global catastrophe will strike. To what extent is climate science political? To what extent are the models being loaded or exaggerated by the scientists themselves to shock the public into preventing possible disasters?
The same concerns apply to economics.
Thanks for another strawman. (You've given me quite the collection.) I never said all economists are right-wing. I'm aware that liberals rely on Keynesian economics and on heterodox models. If I generalized in that respect, I'd have been talking about orthodox, neoliberal, or neoclassical economics.