Recent “grand unified” theories allow for a minute violation of baryon number conservation and in these theories the proton is not absolutely stable. How?
Let me turn it up side down: Why should the proton be stable? or why should the baryonic number be conserved? Quantities are conserved due to the presence of a symmetry, e.g. momentum due to spatial translation; energy due to temporal translation etc. We don't know of any symmetry that gives rise to baryonic number conservation.
But you don't need to go to superstring theories. SUSY, in its R-Parity violating form has two terms that violate baryonic number conservation and lead to proton decay. This prompted, in the 80-ies, few experiments that pushed the lower limit on proton lifetime up by ~4 orders of magnitude.
Indeed, there is no an exact gauge symmetry which could provide a stability of proton. This is why... proton really decays, however, does it extremely slowly. If there is a grand unificatiion at, say, a string scale (10^18 GeV) it may live up to 10^40 years that is well above the present bounds. Also, through either the R+SUSY allowed high-order interactions or non-perturbartively proton lives too long to be observed in terms of its decay products. So, it would hardly be right to look for some fundamental law for the proton stability, because - having no an underlying exact gauge symmetry - it is generically unstable.
Don't know what you mean by "recent" - this is a feature of essentially all GUTs going right back to the first ones. A simple example of how this works is the (now ruled out) SU(5) model of Georgi and Glashow. This model unifies quarks with leptons. For example (d_r, d_g, d_b, \nu_e, e), the red, green and blue down quarks, and the electron neutrino and electron (left chiral) are grouped together in the 5* rep of SU(5). There are gauge bosons that transform the down quarks into the leptons and vice versa. These gauge bosons are the "big sisters" of the ordinary gluons and weak gauge bosons. They disappear from low energy physics because they get large mass ~10^15 GeV by a simple generalisation of the Higgs mechanism.