The precise impact of inherited and somatic mutations on messenger RNA (mRNA) structure remains poorly understood. Recent technological advances that leverage next generation sequencing to obtain experimental structure data, such as SHAPE-MaP (Selective 2' Hydroxyl Acylation by Primer Extension and Mutational Profiling), can reveal structural effects of mutations especially when this data is rigorously incorporated in RNA structural modeling. Here we analyze the ability of SHAPE-MaP to detect the relatively subtle structural changes caused by single nucleotide mutations. We find that allele-specific sorting greatly improved the detection ability of SHAPE-MaP. Thus, we used SHAPE-MaP with a novel combination of clone-free robotic mutagenesis and allele-specific sorting to perform a rapid, comprehensive survey of non-coding somatic and inherited riboSNitches in two cancer-associated mRNAs, TPT1 and LCP1. Combined with rigorous thermodynamic modeling of the Boltzmann suboptimal ensemble we identified a subset of somatic and Lackey 2 inherited mutations that change TPT1 and LCP1 RNA structure, with approximately 14% of all variants identified acting as riboSNitches. To confirm that these in vitro structures were biologically relevant, we tested how dependent TPT1 and LCP1 mRNA structures are on their environments. We performed SHAPE-MaP on TPT1 and LCP1 mRNAs in the presence or absence of cellular proteins and found that both TPT1 and LCP1 have similar overall folds in all conditions. RiboSNitches identified within these mRNAs in vitro are likely to exist under biological conditions. Overall, these data reveal a remarkably robust mRNA structural landscape where differences in environmental conditions and most sequence variants do not significantly alter RNA structural ensembles. Finally, predicting riboSNitches in mRNAs from sequence alone remains particularly challenging; these data will provide the community with a benchmark for further algorithmic development.