Maintaining equilibrium of the gut microbiome is crucial for human health. Diet represents an important and generally accessible natural channel of controlling the nutrients supply to the intestinal microorganisms. Although many studies showed that dietary interventions can specifically modulate gut microbiome composition, further progress of the approach is complicated by interindividual variability of the microbial community response. The reported causes of this variability include the baseline microbiome composition features, but it is unclear whether any of them are intervention-specific. Here, we applied a unified computational framework to investigate the variability of microbiome response measured as beta diversity in eight various dietary interventions using previously published 16S rRNA sequencing datasets. We revealed a number of baseline microbiome features which determine the microbiome response in an intervention-independent manner. One of the most stable associations, reproducible for different interventions and enterotypes, was a negative dependence of the response on the average number of genes per microorganism in the community—an indicator of the community functional redundancy. Meanwhile, many revealed microbiome response determinants were enterotype-specific. In Bact1 and Rum enterotypes, the response was negatively correlated with the baseline abundance of their main drivers. Additionally, we proposed a method for preliminary assessment of the microbiome response. Our study delineats the universal features determining microbiome response to diverse interventions. The proposed approach is promising for understanding the mechanisms of gut microbiome stability and improving the efficacy of personalised microbiome-tailored interventions.