Public perception about the reality of climate change has remained polarized and propagation of fake information on social media can be a potential cause. Homophily in communication, the tendency of people to communicate with others having similar beliefs, is understood to lead to the formation of echo chambers which reinforce individual beliefs and fuel further increase in polarization. Quite surprisingly, in an empirical analysis of the effect of homophily in communication on the level of polarization using evidence from Twitter conversations on the climate change topic during 2007–2017, we find that evolution of homophily over time negatively affects the evolution of polarization in the long run. Among various information about climate change to which people are exposed to, they are more likely to be influenced by information that have higher credibility. Therefore, we study a model of polarization of beliefs in social networks that accounts for credibility of propagating information in addition to homophily in communication. We find that polarization can not increase with increase in homophily in communication unless information propagating fake beliefs has minimal credibility. We therefore infer from the empirical results that anti-climate change tweets are largely not credible.