Producing labels for unlabeled data is error-prone, making semi-supervised learning (SSL) troublesome. Often, little is known about when and why an algorithm fails to outperform a supervised baseline. Using benchmark datasets, we craft five common real-world SSL data scenarios: few-label, open-set, noisy-label, and class distribution imbalance/misalignment in the labeled and unlabeled sets. We propose a novel algorithm called Contrastive Credibility Propagation (CCP) for deep SSL via iterative transductive pseudo-label refinement. CCP unifies semi-supervised learning and noisy label learning for the goal of reliably outperforming a supervised baseline in any data scenario. Compared to prior methods which focus on a subset of scenarios, CCP uniquely outperforms the supervised baseline in all scenarios, supporting practitioners when the qualities of labeled or unlabeled data are unknown.