Because the Peccei-Quinn (PQ) symmetry has to be anomalous to solve the strong CP puzzle, some colored and chiral fermions have to transform nontrivially under this symmetry. But when the Standard Model (SM) fermions are charged, as in the PQ or Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) models, this symmetry ends up entangled with the SM global symmetries, baryon (B) and lepton (L) numbers. This raises several questions addressed in this paper. First, the compatibility of axion models with some explicit B- and/or L-violating effects is analyzed, including those arising from seesaw mechanisms, electroweak instanton interactions, or explicit B- and L-violating effective operators. Second, how many of these effects can be simultaneously present is quantified, along with the consequences for the axion mass and vacuum alignment if too many of them are introduced. Finally, large classes of B- and/or L-violating interactions without impact on axion phenomenology are identified, like, for example, the various implementations of the type-I and -II seesaw mechanisms in the DFSZ context.