The magnetic ground states of rare-earth frustrated magnets can be governed by competing energy scales arising from crystal-field anisotropy, exchange interactions, and long-range dipolar interactions. Here we investigate this interplay in the triangular-lattice antiferromagnet NaBaEr(BO₃)₂ by combining magnetization, specific heat, and neutron scattering measurements. Neutron powder diffraction resolves rotations of the ErO₆ octahedra and supports the lower-symmetry R3̄ structure over the previously proposed R3̄m model. Magnetization measurements and inelastic neutron scattering establish an effective spin-1/2 description of its low-temperature magnetism with pronounced easy-axis anisotropy, arising from a well-isolated Kramers ground-state doublet separated from the first excited crystal-electric-field level by approximately 4 meV. Below T_(rm N)=0.1 K, single-crystal neutron diffraction reveals A-type antiferromagnetic order with the ordered moment predominantly oriented within the ab plane, despite the pronounced paramagnetic easy-axis anisotropy. The estimated dipolar interaction scale is comparable to T_(rm N), and classical dipolar-energy calculations for the observed stacking pattern favor an in-plane moment orientation. These results reveal contrasting crystal-field and dipolar anisotropies in determining the magnetic ground state of NaBaEr(BO₃)₂.