Are antileptons and antibaryons linked? The recent news about the T2K experiment got me thinking: is there any linkage in the Standard Model between the matter and antimatter categories across the families of Standard Model particles? Are antileptons necessarily linked to antibaryons? 
As a specific example: In our universe "matter" is made up of electrons $e^-$ and protons $p$. Antimatter particles are positrons $e^+$ and antiprotons $\bar p$. 
$p$ and $\bar p$ are obviously a matter-antimatter pair, but is there any theoretical reason the $e^-$ is the same type of matter as the $p$? Could there be a universe in which $p$ and $e^+$ are the "matter" particles and $\bar p$ and $e^-$ are the "antimatter" particles?* 
* Besides the fact that obviously that would be a weird universe where you couldn't make atoms. 
 A: 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.
A: Protons and electrons are not composed of the same "type of matter". Electrons i.e. leptons are fundamental particles whereas protons are Hadrons which are compositions of quarks. Quarks and leptons are the fundamental particles.
Also, obviously opposite charges attract so an atom could not be made where you've combined a matter and antimatter as the 'matter pair'. You could argue that possibly you could have $\bar{p}$ and $e^+$. As in antimatter is the new matter but they're are theoretical mechanisms in which matter dominates antimatter in the earlier universe to get what we have today.
They are grouped because their charges are ~equal in magnitude and opposite. Opposite so they attract and experimentally so very close in magnitude.
If you make the argument that the decay of a proton is to a positron and neutral pion (which is hypothetical and not observed yet) you can see why their charges are of equal magnitude and hence why they 'form up together'.
A: This was the first thing Dirac thought of when he produced the Dirac equation which predicts the positron. He thought there might be some hidden loss of symmetry, and that the positron could be the proton. Within a couple of years of the hypothesis, it had been fairly conclusively rejected and Dirac predicted that the anti-electron (as he then termed it) should actually exist. The positron was observed soon afterwards (more strictly, it had already been observed, but not recognised).
A: I'm not departing from the standard model, but I think it can surely be fit in this model. In the Rishon Model they are surely connected. I know it's non-mainstream, but I think it's very plausible. And I let no occasion go by to make propaganda for it.
The model proposes two (!) elementary particles, the T-rishon and the V-rishon. The T rishon has an electric charge of 1/3, a color charge (as in the strong force), and a new charge: the hyper color (which makes the weak force a residue force), who's associated force keeps the rishons tight together.
The electron:   T* T* T* (* means anti)
The neutrino:   V V V
The up quark:   T T V
The down quark: T* V* V*
The three families (muon+neutrino, tau+neutrino, c-quark, s-quark, b-quark, and t-quark) contain the same combination of rishons and are excitations of the electron, electron-neutrino, u-quark and d-quark.
So a proton: T T V / T T V /T* V* V*
A neutron:   T T V / T* V* V*/ T* V* V*
An electron: T* T* T*
A neutrino: V V V
One can see that in the entire Universe there are equal amounts of T's and T*'s, as well as V's and V*'s (6T-6T*, 6V-6V*). No matter-antimatter asymmetry! If we take the mass of the rishons zero, the super color force can hold the T's (T*'s) and V's (V*'s), flying at light speed together, so they have an effective mass. Neutrino's barely have interacted with other particles and still fly with the speed of light, in contrast to electrons and quarks.
In this picture (coming from Quantum Loop Gravity) one can see a similar structure:

Maybe in some parallel Universe (or mirror universe) there are only positrons, anti-protons and -neutrons, and anti-neutrinos). Of course, this has consequences for CPT symmetry.
A: 
What I am trying to ask: is there any reason that p and e− must be grouped together as matter (other than their current abundance in the universe).

The basic and only reason is that the grouping is consistent and unique within the standard model of particle physics, which emerged from a great number of data validating it. It depends on  what has been observed.
