Fairness-aware community detection has recently emerged as an important direction within fair social network analysis. While existing work has begun to integrate fairness constraints into traditional community detection methods, these efforts are limited to single-layer networks, despite many real-world social systems being inherently multilayered. Before extending such methods to multilayer settings, it is critical to clarify how the multilayer network structure affects the feasibility and interpretation of fairness objectives. In this paper, we identify four interrelated dimensions along which fairness-relevant considerations arise: the networked system and its intrinsic or modeling-induced biases, the types of multilayer communities that different methods can detect, the fairness definitions and how the various layers contribute to them, and algorithmic factors that can potentially impact fairness outcomes. By examining how these aspects interact, we provide a foundation for principled method design, and highlight key open challenges, most notably the need for multilayer-specific fairness definitions and comprehensive benchmarking.