Widely linear (WL) receivers are able to fulfill single antenna interference cancellation (SAIC) of one rectilinear (R) (ASK, BPSK) or quasi-rectilinear (QR) (MSK, GMSK, OQAM) co-channel interference (CCI), a function which is operational in GSM handsets in particular. However, in most cases, SAIC technology loses its efficiency if the residual frequency offset (FO) of the CCI is above a very small fraction of the baud rate. It may be the case for airborne communications, due to high differential Doppler shifts. It may also be the case if we try to use SAIC/MAIC receivers to mitigate intrinsic inter-carrier interference (ICI) of FBMC-OQAM waveforms, which are candidate for 5G networks, and for which the ICI FO is equal to 50% of the (real) baud rate. In this context, the purpose of this paper is twofold. The first one is to extend, for an arbitrary propagation channel and from a MLSE-based approach, the SAIC/MAIC concept to R or QR signals with differential FO using WL FRESH filtering. The second one is to analyse both analytically and by simulations the impact of the residual CCI FO on the performance of the proposed SAIC/MAIC receiver