The need to consider the role of social factors in the efficacy of farm management and, consequently, in the onset and persistence of diseases typical to animal farms is increasingly being realized increasingly worldwide. Many risk analysis studies have been conducted to assess the role of various factors in the development of animal diseases; however, very few have accounted for the role of social factors. The aim of this work was to bridge this gap, with the main hypothesis that different socio-economic factors could be valid indicators for the occurrence of different animal diseases. A socio-economic analysis was performed using demographic characteristics of the farmers and data from 44 social indicators released by the Italian Statistician National Institute of Statistics (ISTAT) database. African swine fever (ASF) in wild boars (WB) and domestic pigs and other endemic animal diseases and zoonoses in Sardinia were considered, such as cistic echinococcosis (CE), contagious agalactia (CA), trichinellosis, West Nile disease (WND), and bluetongue (BT). Seven different negative binomial regression models were fitted using the number of cases between 2011–2017. Three indicators—cultural demand, employment rate, and legality—showed a statistically significant association with risk for all the diseases considered, but with varying effects. Some indicators, such as the age and sex of the farmer, material deprivation index, number of farms and animals, micro-criminality index, and rate of reported thefts were common to ASF, CA, trichinellosis, and CE cases. Others such as the forest surface and the energy produced from renewable sources were common to BT, WND, and ASF in WB. Tourism in seasons other than summer was a valid predictor of ASF and trichinellosis, while out-of-region hospital use had a statistically significant role in CE risk identification. These results may help understand the social context in which these diseases may occur and thus guide the design and implementation of additional risk management measures that go beyond well-known veterinary measures.