Proton decay is an affliction particularly common in grand unified theories (GUTs) that seek to combine all three Standard Model forces in a single unified theory, typically a single group representation.
It is typically not a problem in BSM theories that tweak one part or another of the Standard Model in a less comprehensive manner, for example, by introducing heavy right handed neutrinos to support a see saw mechanism for neutrino mass generation and as dark matter candidates, or by adding a fourth generation of Standard Model fermions. Likewise, it is not generally an issue in BSM theories that set forth a theory of quantum gravity or modify gravity, without tinkering with the Standard Model in any significant way.
As the introduction to the Wikipedia article on Proton Decay sums up the situation:
In
particle physics,
proton decay is a
hypothetical form of
radioactive decay in which the
proton decays into lighter
subatomic particles, such as a neutral
pion and a
positron.
[1] There is currently no experimental evidence that proton decay occurs.
According to the
Standard Model, protons, a type of
baryon, are stable because
baryon number (
quark number) is
conserved (under normal circumstances; see
chiral anomaly for exception). Therefore, protons will not decay into other particles on their own, because they are the lightest (and therefore least energetic) baryon.
Some beyond-the-Standard Model
grand unified theories (GUTs) explicitly break the baryon number symmetry, allowing protons to decay via the
Higgs particle,
magnetic monopoles or new
X bosons with a half-life of 10^31 to 10^36 years.
The GUTs allow proton decay (which violated baryon number conservation), neutrinoless double beta decay (which violated lepton number conservation), and flavor changing neutral currents (which can also violate conservation of one or both of these numbers) in large part by design.
These features are designed into GUTs despite the non-observation of any instance of either conservation of baryon number or conservation of lepton number, because GUT designers want to include a mechanism by which the matter-antimatter asymmetry of the universe can be reproduced following a Big Bang out of pure energy in which baryon number and lepton number are both zero and all subsequent processes respect the laws of physics set forth in the GUT.
In the Standard Model, separate conservation of lepton number and baryon number implies that those numbers have remained unchanged in the universe since the universe entered an epoch which is within the domain of applicability of the Standard Model which according to conventional cosmology estimates begins about 10 seconds after the Big Bang and perhaps even as early as 1 second after the Big Bang.
https://en.wikipedia.org/wiki/Chronology_of_the_universe
But, if you are designing a GUT that is supposed to have a domain of applicability at the extremely high energies that existed in those first one to ten seconds after the Big Bang which is outside the domain of applicability of the Standard Model, and you believe that B=0 and L=0 is the only natural starting point for the Big Bang, then you need to design in processes that violate separate B and L conservation (substituting a global conservation of B-L is the usual choice) then you are going to get processes that violate separate B and L conservation like proton decay, neutrinoless double beta decay, and flavor changing neutral currents, which are not observed.
The Standard Model actually does have one or two processes that conserve B-L but not B and L separately, but those processes are not common enough, even at the extreme energy levels of the first ten seconds after the Big Bang, to generate to observed matter-antimatter asymmetries in the universe.
Another reason to design violations of B and L conservation into a GUT is that this makes it possible to have Majorana mass neutrinos which are greatly favored over Dirac mass neutrinos by GUT designers and theoretical physicists, but which violate L conservation and give rise to neutrinoless double beta decay which has not been observed either.
Of course, then you have to have some mechanism that shuts off or dramatically suppresses these processes in circumstances within the domain of applicability of the Standard Model that puts these events beyond detection with current experiments to make your GUT a viable candidate to describe reality. The first GUTs didn't even come close because their designers didn't realize that proton decay would turn out to be a problem. Later GUT designers tweaked their models to escape current experimental bounds but were over optimistic about the likelihood that B and L violation would show up just beyond current experimental bounds. Current GUT designers are well aware of the problems involved in allowing B and L violation that has been experimentally ruled out to quite extreme levels, but are overconstrained because if the B and L violation threshold is set too high, the GUT won't be able to reproduce the matter-antimatter asymmetry that is observed in our universe.
