Molecular evolutionary studies of genomic base composition and GC content have a long unresolved history of frequency-based methods of analysis applied only to DNA sequence data. However, this tradition ignores the physicochemical impacts of mutation that can affect the molecular dynamics of nucleic acid polymers. This is especially problematic during transcription, where mutation can influence the complex interactions at play in chromatin-mediated genomic regulation. Here, we investigate the two primary biophysical constraints required of eukaryotic transcription; a flexible/nuclear-compacted DNA and a stable/non-self-reactive RNA; both features which can be significantly affected by the molecular evolution of GC content in the genome. We utilize a 2x448 core Tesla supercomputer to conduct 2000 nanosecond scale GPU accelerated molecular dynamic simulations of mutation in randomized DNA and RNA sequence backgrounds, where we investigate mutational impacts on molecular dynamics while controlling for varying GC content. Additionally, in Saccharomyces yeast alignments, we employ simulations of neutral evolution to locally map natural selection acting on DNA flexibility and RNA stability. We find that different classes of mutation have very different GC-dependent impacts on dynamics, defined via shifts in atomic fluctuation and correlation, and indicating that GC-related molecular dynamics of nucleic acids are correlated and evolvable. In DNA, we report that low GC generally amplifies mutational impacts on molecular dynamics while increasing the impact of transversion over transition, providing a potent functional evolutionary constraint that may form a basis for transition bias observed in most genomes. In RNA, we observe that the molecular dynamic impacts of mutation depend largely upon their impact on uracil, the most interactive of the nucleobases. In Saccharomyces yeasts, we find evidence that many yeast genes have effectively decoupled the biophysical relationship between DNA flexibility and RNA stability by elevating GC. We also report a significant genome-wide signature whereby TFBS consensus sequences are partly defined by mutational impacts on DNA flexibility. We conclude that the historical assumption of genetic abstraction in molecular evolution is quite limiting, especially regarding the role of nucleic acid polymer biophysics in interpreting broad patterns in molecular evolution related to genome packaging and control of transcription.