In the context of brain tumor characterization, we focused on two key questions: (a) stability of radiomics features to variability in multiregional segmentation masks obtained with fully-automatic deep segmentation methods and (b) subsequent impact on predictive performance on downstream tasks: IDH prediction and Overall Survival (OS) classification. We further constrained our study to limited computational resources setting which are found in underprivileged, remote, and (or) resource-starved clinical sites in developing countries. We employed seven SOTA CNNs which can be trained with limited computational resources and have demonstrated superior segmentation performance on BraTS challenge. Subsequent selection of discriminatory features was done with RFE-SVM and MRMR. Our study revealed that highly stable radiomics features were: (1) predominantly texture features (79.1%), (2) mainly extracted from WT region (96.1%), and (3) largely representing T1Gd (35.9%) and T1 (28%) sequences. Shape features and radiomics features extracted from the ENC subregion had the lowest average stability. Stability filtering minimized non-physiological variability in predictive models as indicated by an order-of-magnitude decrease in the relative standard deviation of AUCs. The non-physiological variability is attributed to variability in multiregional segmentation maps obtained with fully-automatic CNNs. Stability filtering significantly improved predictive performance on the two downstream tasks substantiating the inevitability of learning novel radiomics and radiogenomics models with stable discriminatory features. The study (implicitly) demonstrates the importance of suboptimal deep segmentation networks which can be exploited as auxiliary networks for subsequent identification of radiomics features stable to variability in automatically generated multiregional segmentation maps.