Manufacturing systems develop toward cloud-edge collaboration where manufacturing and computation are tightly coupled. Under this circumstance, large-scale hybrid tasks that include manufacturing and computational tasks need to be collaboratively scheduled among heterogeneous resources. This paper solves the hybrid task scheduling problem in cloud-edge collaborative manufacturing systems with FCRN-assisted random differential evolution (F-RDE). First, we establish a system model for hybrid task scheduling with the objective of minimizing the total makespan and energy consumption. This model includes four types of time constraints between the hybrid tasks. The scheduling of such hybrid tasks has received limited attention in existing research. Next, large-scale decision variables are encoded into the evolutionary chromosomes. To generate offspring chromosomes, we construct four differential evolution operators that are randomly selected during the search process. Furthermore, we propose the fully convolutional regression network (FCRN) as a novel surrogate model to accelerate fitness evaluation. To enhance the integration of FCRN and the differential evolution procedure, we employ three strategies: chromosome folding, top-K re-evaluation, and three training modes. The FCRN surrogate can effectively represent chromosomes with up to 12000 dimensions and achieve generalization across diverse scheduling cases. This leads to reduced solving time and enhanced fitness estimation accuracy. Numerical experiments on three hybrid task scheduling cases validate the superiority compared to the other twelve scheduling algorithms, and the proposed FCRN surrogate can save at most 43% of solving time.