The ability of machine learning (ML) classification models to resist small, targeted input perturbations -- known as adversarial attacks -- is a key measure of their safety and reliability. We show that floating-point non-associativity (FPNA) coupled with asynchronous parallel programming on GPUs is sufficient to result in misclassification, without any perturbation to the input. Additionally, we show that standard adversarial robustness results may be overestimated up to 4.6 when not considering machine-level details. We develop a novel black-box attack using Bayesian optimization to discover external workloads that can change the instruction scheduling which bias the output of reductions on GPUs and reliably lead to misclassification. Motivated by these results, we present a new learnable permutation (LP) gradient-based approach to learning floating-point operation orderings that lead to misclassifications. The LP approach provides a worst-case estimate in a computationally efficient manner, avoiding the need to run identical experiments tens of thousands of times over a potentially large set of possible GPU states or architectures. Finally, using instrumentation-based testing, we investigate parallel reduction ordering across different GPU architectures under external background workloads, when utilizing multi-GPU virtualization, and when applying power capping. Our results demonstrate that parallel reduction ordering varies significantly across architectures under the first two conditions, substantially increasing the search space required to fully test the effects of this parallel scheduler-based vulnerability. These results and the methods developed here can help to include machine-level considerations into adversarial robustness assessments, which can make a difference in safety and mission critical applications.