In this letter, we propose an iterative soft interference cancellation scheme for intra-cluster (ICL) and out-of-cluster (OCL) interference mitigation in user-centric clustered cell-free massive multiple-antenna networks. We propose a minimum mean-square error receive filter with a novel modified parallel interference cancellation scheme to mitigate ICL and OCL interference. Unlike prior work, we model the OCL interference and devise a least squares estimator to perform OCL interference estimation. An iterative detection and decoding scheme that adopts low-density parity check codes and incorporates the OCL interference estimate is developed. Simulations assess the proposed scheme against existing techniques in terms of bit error rate performance.