We interpret attitudes towards science and pseudosciences as cultural traits that diffuse in society through communication efforts exerted by agents. We present a tractable model that allows us to study the interaction among the diffusion of an epidemic, vaccination choices, and the dynamics of cultural traits. We apply it to study the impact of homophily between pro-vaxxers and anti-vaxxers on the total number of cases (the cumulative infection). We show that, during the outbreak of a disease, homophily has the direct effect of decreasing the speed of recovery. Hence, it may increase the number of cases and make the disease endemic. The dynamics of the shares of the two cultural traits in the population is crucial in determining the sign of the total effect on the cumulative infection: more homophily is beneficial if agents are not too flexible in changing their cultural trait, is detrimental otherwise.