Is there a reason for the names we use? Would the world work differently if we used different names? As Feynman used to emphasize, you may call anything anything you like, as long as others understand you: it is a communication issue.
On the objective side, you might speculate about alternate universes, and alternate principles leading to them all you like, but as you observed, such universes would be surprising. By contrast, a universe with $e^+, \bar p, \bar n $ appears tenable, given the physics we know, and not different than ours. (Well, somewhat: the SM charts in schools would have those particles in them instead of our particles!)
In our world, p,n,e comprise our matter. Unstable conjugates thereof discovered only in the 20th century are termed antimatter, and the corresponding quarks are termed quarks and not antiquarks. The charge and structure of the remaining unstable particles are named after those. Neutrinos, when discovered, fell into the same scheme.
e and p are not "the same type of matter", and no, they are not "linked" except by the facts on the ground. They happen to be the lightest extant charged lepton (lepton number L) and baryons (baryon number B). Our world apparently mostly preserves B and L, but not quite; but almost certainly B-L (technical: anomaly free). You may have been puzzled by the facile posters of the SM families in schools. Such posters are pedagogical mnemonics, ordering matter fermions by mass, so even the linkage between e with u,d is a matter of convenience: You might, counterintuitively, associate e with t,b. As long as you describe these fermions correctly, the inevitability of terms you use for them cannot escape the realm of mere opinion.
To be clear: the SM families with gauge-anomalies cancelling are e,ν, u,d, etc, (sparing you the hypothetical cross-linkage above), and their antifermion families. That's how they fit. Calling these leptons anew anti-leptons leaving all their gauge charges untouched and using them in your fermion family, instead, would not change a thing. (Anomalies and their cancelations only care about such charges, and not the fermion or lepton number employed in referring to them. In fact, in the SU(5) GUT, leptons and antiquarks are already arrayed together in the smallest representation, to the disorientation of some learners.)
You'd have more fast-talking to do, about this SM peculiarity, and eventually somebody would "brilliantly" propose reversing the re-classification of these "leptons" to "anti leptons", so the triangle loops of all matter fermions and antimatter antifermions in each anomaly split into two separately cancelling groupings. But this would be a strictly terminological advance.