When we talk about future climate change refugees, the picture that comes to mind is starving people looking to leave a drought stricken country whose economic system has failed. Tragic, but within the international law system, these would be economic migrants who are not entitled to refugee status. The international community would try to provide some food aid, but it would play out like so many droughts or other food crises because of crop failures in Africa in the past. When you look at climate change from a national security perspective, Syria is a much more likely scenario. Climate change destabilizes a country in the band of countries from Syria through Bangladesh that are already politically unstable and are surrounded by unstable neighbors, some of which are nuclear armed. When there is no stable bordering country able to receive them, refugees pour across borders into hostile states, triggering international conflicts. Refuges from states that descend into chaos will be protected under the the 1951 Refugee Convention. (They may not qualify for the US standard, which seems to require individual groups for persecution, rather than general risk of being killed.)
Kelley, C. P., Mohtadi, S., Cane, M. A., Seager, R. & Kushnir, Y. (2015). Climate change in the Fertile Crescent and implications of the recent Syrian drought. Proceedings of the National Academy of Sciences, 112(11), 3241–3246. National Acad Sciences.