Climate change research relies heavily on complex computational tools to model environmental processes, analyse large datasets, and inform policy. Current scientific computing practices pose significant barriers to entry, particularly for interdisciplinary researchers and those in low and middle-income countries (LMICs). Challenges include steep learning curves, limited access to expert support, and difficulties using legacy or under-documented software. Drawing on real-world experiences, we identify recurring obstacles in the usability, accessibility, and sustainability of scientific software. Our analysis of real-world case studies highlights that current approaches to scientific software development disadvantage interdisciplinary and LMIC researchers. We propose specific mechanisms to address these inequities, including: improved documentation, domain-aware training programs, automation for diverse hardware environments, domain-specific languages, and hybrid support communities. These measures should be integrated into grant funding requirements to ensure sustainability beyond initial project periods, transforming scientific software from short-lived outputs into accessible research infrastructure. By reimagining scientific programming as a shared public good, we can lower entry barriers and foster a more inclusive, equitable climate research ecosystem.