Causal discovery is a highly promising tool with a broad perspective in the field of biology. In this study, a causal structure robustness assessment algorithm is proposed and employed on the causal structures obtained, based on transcriptomic, proteomic, and the combined datasets, emerging from a quantitative proteogenomic atlas of 15 sweet cherry (Prunus avium L.) cv. ‘Tragana Edessis’ tissues. The algorithm assesses the impact of intervening in the datasets of the causal structures, using various criteria. The results showed that specific tissues exhibited an intense impact on the causal structures that were considered. In addition, the proteogenomic case demonstrated that biologically related tissues that referred to the same organ induced a similar impact on the causal structures considered, as was biologically expected. However, this result was subtler in both the transcriptomic and the proteomic cases. Furthermore, the causal structures based on a single omic analysis were found to be impacted to a larger extent, compared to the proteogenomic case, probably due to the distinctive biological features related to the proteome or the transcriptome. This study showcases the significance and perspective of assessing the causal structure robustness based on omic databases, in conjunction with causal discovery, and reveals advantages when employing a multiomics (proteogenomic) analysis compared to a single-omic (transcriptomic, proteomic) analysis.