Based on pruning techniques that interpret polar codes as low-density parity-check-like (LDPC-like) codes, this paper develops novel belief propagation (BP)-based decoders utilizing the concept of schedule diversity. By analyzing the impact of hidden variable nodes (VNHs), scheduling algorithms that guarantee fast convergence speeds and superior error performance are devised for the LDPC-like sparse factor graph (SPF), incorporating both standard sequential scheduling (SSS) and informed dynamic scheduling (IDS) algorithms. To further enhance error performance, cyclic redundancy check (CRC) bits are integrated into the LDPC-like SPF, and random update sequences are introduced to reduce computational complexity while implementing schedule diversity. Inspired by belief propagation list decoding, the proposed approaches eventually update messages in the LDPC-like SPF according to various schedules, thereby producing diverse decoding outcomes. Compared to the CRC-aided successive cancellation list (CA-SCL) decoder and benchmark soft-output decoders in the literature, the proposed schemes achieve comparable or improved error performance while reducing computational complexity in the high SNR region. These results serve as preliminary findings on the BP algorithm over LDPC-like SFGs and provide useful insights for the design and practical improvement of polar decoders.