You don't have to put trust in a field to do an overview of the existing literature and show how and where it is wrong. Neither philosophy or mathematics, for example, don't follow the "scientific method" (let's assume the Anglophone conception as opposed to Wissenschaft for the sake of arument), yet I would hope that people would rightly call out a post on utilitarianism that doesn't take into account arguments from the last twenty years, or an argument against metaphysics that stops at Hume, and they'd be skeptical of a proof of the Riemann hypothesis expressed in all but the terms of mathematicians.

If you're more convinced by my mathematics example than my philosophy one, it just shows that this isn't about the scientific method at all, but standards of rigor in argumentation, which soft sciences are perfectly capable of, at least internally within frameworks. In that case, all it would take is for the author to mention which framework they believe has the most explanatory power, and why.

Lastly, I fail to see why this would be such an issue in the first place; as an example, take a claim like "viewing pornography is associated with misogynistic attitudes", or even more strongly, that pornograhy causes such attitudes. The fact that it is a broad claim, that relies on population samples and indirect measurement, does not make the research into the topic (both in support and in denial of the claim) any less valid to be ignorant about, if you're writing an essay on whether porn should be censored or not.

Different epistemic standards are not an excuse for ignorance. "Not as authoritive" is not the same as "no authority at all", and it's especially not the same when the essay in question itself is engaging in that topic.