$U(1)$ extensions of the minimal supersymmetric (SUSY) standard model (MSSM) there can solve the $\mu$-problem of the MSSM and give extra $F$ and $D$ term contributions to the Higgs mass. For such models there is a simple mechanism that splits the $Z^\prime$ mass from the SUSY scale allowing for sfermions which are significantly lighter that the $Z'$ mass. This mechanism can also result in light pseudoscalar state, allowing the $125\,\mbox{GeV}$ SM-like Higgs boson to decay into a pair of such pseudoscalars. We study these decays within $E_6$ inspired SUSY models with exact custodial symmetry that forbids tree-level flavor-changing transitions and the most dangerous baryon and lepton number violating operators. We find that the branching ratio of the lightest Higgs boson decaying into a pair of light pseudoscalar states can be large.