Traditionally, meat and dairy products have been important protein sources in the human diet. Consumers are eating more plant-based proteins, which is reflected in current market trends. Assessing how alternative proteins are processed and their impact on food safety helps realize market opportunities while ensuring food safety. In this review, an analysis of the food safety hazards, along with current industry trends and processing methods associated with alternative proteins for meat and dairy products for the European Union market is described. Understanding the effects of processing and safety alternative proteins is paramount to ensuring food safety and understanding the risks to consumers. However, the data here is limited. With the expected further increase in protein alternatives in consumers’ diets, the risk of food allergens is apparent. The occurrence of processing contaminants in plant-based alternatives may occur, along with anti-nutritional compounds, which interfere with the absorption of nutrients. Further, typical food safety hazards related to the plant, the product itself, or processing are relevant. Although hazards in insects and seaweed are being addressed, other protein alternatives like cultured meat and SCPs warrant attention. Our findings can aid industry and governmental authorities in understanding current trends and prioritizing hazards for future monitoring.