Vaccination is widely recognized as the most effective way of immunization against many infectious diseases. However, unfounded claims about supposed side effects of some vaccines have contributed to spread concern and fear among people, thus inducing vaccination refusal. For instance, MMR vaccine coverage has undergone an important decrease in a large part of Europe and US as a consequence of erroneously alleged side effects, leading to recent measles outbreaks. In this work, we propose a general agent-based model to study the spread of vaccination behavior in social networks, not as an isolated binary opinion spreading on it, but as part of a process of cultural dissemination in the spirit of Axelrod's model. We particularly focused on the impact of a small anti-vaccination movement over an initial population of pro-vaccination social agents. Additionally, we have considered two classes of edges in the underlying social network: personal edges able to spread both opinions and diseases; and the non-personal ones representing interactions mediated by information technologies, which only allow opinion exchanges. We study the clustering of unvaccinated agents as a dynamical outcome of the model, together with its direct relation with the increase of the probability of occurrence and the final size of measles outbreaks. Finally, we illustrate the mitigating effect of a public health campaign, represented by an external field, against the harmful action of anti-vaccination movements. We show that the topological characteristics of the clusters of unvaccinated agents determine the scopes of this mitigating effect.