Understanding the nuances of climate change on buildings in desert areas is a timely topic with several socioeconomic implications. This study quantifies the impacts of future climate variability and extreme events on the optimal design of renewable energy systems (RES) for buildings in Saudi Arabia. A comprehensive framework integrating multi-model climate projections, extreme event analysis, and stochastic optimization is developed to evaluate system reliability and economic performance under future climate uncertainty. Hourly downscaled climate data spanning 2025-2099 across multiple Shared Socioeconomic Pathways (SSP) are considered, and stochastic optimization is used to determine RES configurations that minimize life cycle cost (LCC) across all scenarios. Analyses are conducted at hourly resolution over three future 25-year periods: 2025-2049, 2050-2074, and 2075-2099. Results indicate that differences between climate scenarios become more pronounced in the late-century period (2075-2099), leading to increased sensitivity of optimal RES design to climate conditions. The stochastic design ensures higher operational reliability than systems optimized solely for a high-emission scenario, with a 3.1% increase in LCC. Relative to the sustainable scenario, the high-emission scenario requires larger RES capacities, particularly in battery storage, resulting in a 20% higher LCC. Accounting for extreme events from an additional 24 scenarios from multiple climate models increases the LCC by 31.7%, highlighting the cost of resilience in an uncertain future climate.