The term core microbiome describes microbes that are consistently present in a particular habitat. If the conditions in that habitat are highly variable, core microbes may also be considered to be ecological generalists. However, little is known about whether metabolic competition and microbial interactions influence the ability of some microbes to persist in the core microbiome while others cannot. We investigated microbial communities at three sites in the guts of European seabass under four dietary conditions. We identified generalist core microbial populations in each gut site that are shared across fish, present under multiple diets and persistent over time. We found that core microbes tend to show synergistic growth in co-culture, and low levels of predicted and validated metabolic competition. Within core microbial species, we found high levels of intraspecific variability and strain-specific habitat specialization. Thus, both intraspecific variability and interspecific facilitation may contribute to the ecological stability of the animal core microbiome. © 2019, The Author(s), under exclusive licence to Springer Nature Limited.