Plastic is made from fossil fuels, which is plastic’s biggest connection to climate change (See: https://www.plasticseurope.org/en/about-plastics/what-are-plastics/how-plastics-are-made). Also, the percentage of global greenhouse gases from plastic production is expected to increase steadily according to the International Energy Agency.
The Washington State Legislature is considering several bills aimed to reduce the use of plastics within the state. See the WA Climate Legislation site to learn more about those bills.
References relating to the intersection of Climate Change and Plastics: