My feeling is that all "soft" sciences should be allowed on this site.
As a hard scientist myself, I understand the reasoning to label soft sciences as unscientific. By the standards of hard sciences, they're hardly rigorous. I know that in my everyday speech, if I used the term "science", it would basically never refer to these areas.
On the other hand, if you look at modern day research in social sciences, it is quite a bit more rigorous than e.g. 12th century chemistry research. And perhaps in 50 or 100 years, we may have a far better understanding of cognitive science as computational neural models become increasingly sophisticated. Saying that e.g. economics or psychology isn't a science right now is ignoring almost the entirety of history (the focus of this site) where chemistry, biology, and physics wouldn't meet today's scientific standards.
If we're going to start trying to define what does/doesn't count as science, we're opening up the door to all sorts of challenges of scientific merit that have no place here. Just from my own field of physics, I've heard (reputable) scientists accuse a number of topics of being "unscientific", including high-temperature superconductivity, loop quantum gravity, string theory, inflationary cosmology, supersymmetric phenomenology, stellar evolution models, all of soft condensed matter research, exoplanet astronomy, and all numerical simulations. I have my own opinions on those, but I don't think this is the place to debate which of them is "science" (or even which is "good science"). We should be allowed to ask and answer questions about the history of all of these things. There's really no difference between that and economics or psychology.
Hence, this is the wrong way to define "History of Science" for the purposes of this site. We're looking at the current state of knowledge, determining what aspects count as "science", and then looking at their history. The intermediate step of defining what counts as science is both contentious and unnecessary, and risks casting out entire fields. There are already active professional historians of science, who publish in journals specializing on history of science. We can empirically define "History of Science" to be the subfield of history which is studied by historians of science, avoiding the need to define what is/isn't "valid" science almost completely.
And based on that, yes, soft/social sciences including economics should be included here. But I don't think we're going to be swamped by questions about the Oedipus Complex or Mercantilism. If anything, I suspect we'll have trouble getting anyone who wants to ask about these topics (given our current state of affairs), but if someone does, I don't think we should kick them out if they have a good question.