We study the decays of J/ψ and ψ(3686) to the final states Σ(1385)⁰ Σ̅(1385)⁰ and Ξ⁰ Ξ̅⁰ based on a single baryon tag method using data samples of (1310.6 ± 7.0) x 10⁶ J/psi and (447.9 ± 2.9) x 10⁶ ψ(3686) events collected with the BESIII detector at the BEPCII collider. The decays to Σ(1385)⁰ Σ̅(1385)⁰ are observed for the first time. The measured branching fractions of J/ψ and ψ(3686) to Ξ⁰ Ξ̅⁰ are in good agreement with, and much more precise than, the previously published results. The angular parameters for these decays are also measured for the first time. The measured angular decay parameter for J/ψ → Σ(1385)⁰ Σ̅(1385)⁰, α = -0.64 ± 0.03 ± 0.10, is found to be negative, different to the other decay processes in this measurement. In addition, the "12% rule" and isospin symmetry in the decays of J/ψ and ψ(3686) to Ξ⁰ Ξ̅⁰ and Σ(1385) Σ̅(1385) are tested.