Perhaps you should look harder. The dominant approach in economics for 20 years has been to reject correlational studies and try very hard to get at casuality, by:
* Running randomised controlled trials, often at scale (see eg Esther Duflo);
* Laboratory experiments, which have provided a body of robust paradigms and results;
* Seeking natural experiments;
* Statistical techniques like regression discontinuity and instrumental variables.
There's plenty of bad work in the social sciences. So is there elsewhere in the natural sciences (cough Lancet). There's plenty of good work too.
I did not want to imply that social science studies are non-rigorous, I was actually trying to defend their scientific nature, but with an incorrect phrasing.
Indeed, in Econ grad school I learned a lot about control theory, statistics, dynamic programming, etc. But I was never told to read Foucault, Levi-Strauss or even Marx - something that sociologists and other people in humanities usually have at least a basic understanding of.
If we judge what is science by level of quantitative rig our then economics is the only social science.
But you are right about what happens next: you top it off with academically uneducated (or simply unaware of scientific rigour) politicians like Trump (he's just an obvious example, far from being the only one) making calls on different social topics.