The holistic green energy transition of non-interconnected islands faces several challenges if all the energy sectors are included, i.e., electricity, heating/cooling, and mobility. On the one hand, the penetration of renewable energy systems (RES) is limited due to design restrictions with respect to the peak demand. On the other hand, energy-intensive heating and mobility sectors pose significant challenges and may be difficult to electrify. The focus of this study is on implementing a hybrid Wind−PV system on the non-interconnected island of Anafi (Greece) that utilizes surplus renewable energy production for both building heating through heat pumps and hydrogen generation. This comprehensive study aims to achieve a holistic green transition by addressing all three main sectors—electricity, heating, and transportation. The produced hydrogen is utilized to address the energy needs of the mobility sector (H2 mobility), focusing primarily on public transportation vehicles (buses) and secondarily on private vehicles. The overall RES production was modeled to be 91,724 MWh with a RES penetration of 84.68%. More than 40% of the produced electricity from RES was in the form of excess electricity that could be utilized for hydrogen generation. The modeled generated hydrogen was simulated to be more than 40 kg H2/day, which could cover all four bus routes of the island and approximately 200 cars for moderate use, i.e., traveled distances of less than 25 km/day for each vehicle.