The Antarctic ice sheet (AIS) lies on a solid Earth that displays large spatial variations in rheological properties, with a thin lithosphere and low-viscosity upper mantle (weak Earth structure) beneath West Antarctica and an opposing structure beneath East Antarctica. This contrast is known to have a significant impact on the ice-sheet grounding-line stability. Here, we embed within an ice-sheet model a modified glacial-isostatic Elastic Lithosphere-Relaxing Asthenosphere model that considers a dual pattern for the Earth structure beneath West and East Antarctica supplemented with an approximation of gravitationally consistent geoid changes, allowing to approximate near-field relative sea-level changes. We show that this elementary GIA model captures the essence of global Self-Gravitating Viscoelastic solid-Earth Models (SGVEMs) and compares well with both SGVEM outputs and geodetic observations, allowing to capture the essential features and processes influencing Antarctic grounding-line stability in a computationally efficient way. In this framework, we perform a probabilistic assessment of the impact of uncertainties in solid-Earth rheological properties on the response of the AIS to future warming. Results show that on multicentennial-to-millennial timescales, spatial variability in solid-Earth deformation plays a significant role in promoting the stability of the West Antarctic ice sheet (WAIS). However, WAIS collapse cannot be prevented under high-emissions climate scenarios. On longer timescales and for unmitigated climate scenarios, continent-wide mass loss projections may be underestimated because spatially uniform Earth models, as typically considered in numerical ice sheet models, will overestimate the stabilizing effect of GIA across East Antarctica, which is characterized by thick lithosphere and high upper-mantle viscosity.