We develop a robust multiuser detector for a Frequency Division Multiplexing (FDM) system where each user employs a binary continuous phase modulation (CPM) generated through a low-cost transmitter, thus characterized by a significant modulation index uncertainty, and sent over a channel affected by phase noise. In this FDM system the spectral efficiency can be increased by reducing the spacing between two adjacent channels. The proposed receiver is designed by adopting a simplified representation of a binary CPM signal with the principal component of its Laurent decomposition and is obtained by using the framework based on factor graphs and the sum-product algorithm. This detector can be used for iterative detection/decoding of a coded scheme in which each user employs a binary CPM modulator serially concatenated with an outer encoder through a pseudo-random interleaver. It does not require an explicit estimation of the modulation index nor of the channel phase and is very robust to large uncertainties of the nominal value of the modulation index.