Should chemistry students worry about quarks and such?
Is an understanding of chemistry fundamentals likely to become out of date when the textbooks start to include quarks, leptons and the dozens of other sub-atomic particles?


Well, the general chemisty books do already include leptons, at least electrons and usually positrons.

Other than protons, neutrons, electrons and positrons (and photons), I think that when discussing beta decay and electron capture, neutrinos and antineutrinos should be included, otherwise the nuclear reactions aren't really balanced (lepton number must be conserved).  Alternatively, the general chemistry books could omit all discussion of nuclear reactions, as being physics. 

Other than that, I think the rest of the particles can wait for physics class, rather than general chemistry class.

Beyond general chemistry, other particles are sometimes discussed in more advanced chemistry books, such as quantum chemistry texts, where examples involving muons are common.  

For some chemistry topics, such as isotope differences in rotational-vibrational spectra of small molecules distinction between fermions and bosons is critical.  Trying to explain the difference between fermions and bosons (and Fermi-Dirac statisitics vs Bose-Einstein statistics vs Boltzmann statistics) naturally leads to discussion of the standard model and the particles in the standard model.  So by the time a student gets to physical chemistry, around the third year of college, they should have some understanding of the standard model.