Let's say you "primafy" a general principle when you seek to elevate it to the level of a first principle. For example, one might start from the general principle that stealing is wrong, and foolishly primafy it (abstracting away all the essential details of institutional context) to yield propertarianism.
Any systematic moral theorizing is likely to involve some 'primaficiation' -- for a more sympathetic example, utilitarians elevate the principle that human welfare matters -- but we should at least be wary of overly hasty instances of this move. It's one thing to determine a first principle after careful and systematic reflection, and quite another to leap to the conclusion that something is a first principle just because it's a general principle we recognize in everyday life. It's the latter mistake that I want to warn against.
One common mistake in this vicinity is to primafy rights, perhaps assuming that their practical priority translates into theoretical priority. But this is just a mistake. What rights we ought to institute depends on contingent facts about our situation (in particular, which 'rights' would actually serve to make people better off -- obviously a contingent matter). For all their practical importance, rights are a merely surface-level moral phenomena that emerge from (rather than ground) our fundamental moral theorizing.
More generally, people commonly take their everyday moral sensibility and seek to directly apply it in radically different contexts -- contexts to which their sensibilities are not at all attuned. They seek to evaluate economic policies, for example, according to whether they seem "fair", when consequentialist evaluation is far more fitting. Some make silly claims about "deserving" their pre-tax income in some strong sense which is supposed to render taxation a form of "theft". And much political philosophy has traditionally taken as its starting point the general principle that we shouldn't coerce each other, and so -- by elevating this, out of context, to the level of a first principle -- concluded that any government action requires some special justification (saying it may only do things that are required by justice, for example).
All of this, it seems to me, results from a simple failure to distinguish 'internal' and 'external' moral questions. There are certain norms or principles are appropriate within the context of our everyday lives, but not necessarily in other contexts (e.g. when it comes to assessing the institutional structure that stands behind our everyday interactions). So it would be a mistake to 'primafy' a merely internal principle -- pulling it out of context and treating it as though it were a universally applicable 'first principle'. Moral and political thought would be much improved by bearing this in mind.