Human gut microbial dynamics are highly individualized, making it challenging to link microbiota to health and to design universal microbiome therapies. This individuality is typically attributed to variation in host genetics, diets, environments and medications but it could also emerge from fundamental ecological forces that shape microbiota more generally. Here, we leverage extensive gut microbial time series from wild baboons-hosts who experience little interindividual dietary and environmental heterogeneity-to test whether gut microbial dynamics are synchronized across hosts or largely idiosyncratic. Despite their shared lifestyles, baboon microbiota were only weakly synchronized. The strongest synchrony occurred among baboons living in the same social group, probably because group members range over the same habitat and simultaneously encounter the same sources of food and water. However, this synchrony was modest compared to each host's personalized dynamics. In support, host-specific factors, especially host identity, explained, on average, more than three times the deviance in longitudinal dynamics compared to factors shared with social group members and ten times the deviance of factors shared across the host population. These results contribute to mounting evidence that highly idiosyncratic gut microbiomes are not an artefact of modern human environments and that synchronizing forces in the gut microbiome (for example, shared environments, diets and microbial dispersal) are not strong enough to overwhelm key drivers of microbiome personalization, such as host genetics, priority effects, horizontal gene transfer and functional redundancy.