The energy optimization of the reentrant hybrid flow shop scheduling problem (RHFSP) represents a critical challenge in the field of sustainable manufacturing. In this study, a bi-objective mixed-integer linear programming model is formulated to minimize both makespan and total energy consumption. Based on this model, a clustering and entropy-guided unsupervised learning multi-objective evolutionary algorithm (CEUL-MOEA) is developed. The algorithm establishes a cooperative dual-population framework for exploration and exploitation. Both populations are initialized using dual encoding-decoding rules and diversified heuristic methods. In the exploitation population, an objective-driven destruction–reconstruction strategy is employed to enhance local search accuracy, while the exploration population incorporates a co-evolutionary crossover strategy to improve population diversity. Furthermore, an unsupervised learning-based clustering and entropy-guided neighborhood search strategy is integrated to overcome the randomness and arbitrariness of conventional neighborhood perturbations. In addition, specific right-shift conditions are proposed in the right-shift energy-saving strategy, which significantly reduces idle energy consumption without affecting the makespan. Experimental results based on 275 benchmark instances demonstrate that the CEUL-MOEA significantly outperforms mainstream comparative algorithms in both convergence speed and solution set distribution, with the GD and IGD metrics reduced by 89% on average and the HV metric increased by 56% on average.