We study the design of receivers in extra-large scale MIMO (XL-MIMO) systems, i.e. systems in which the base station is equipped with an antenna array of extremely large dimensions. While XL-MIMO can significantly increase the system's spectral efficiency, they present two important challenges. One is the increased computational cost of the multi-antenna processing. The second is the variations of user energy distribution over the antenna elements and therefore spatial non-stationarities in these energy distributions. Such non-stationarities limit the performance of the system. In this paper, we propose a distributed receiver for such an XL-MIMO system that can address both challenges. Based on variational message passing (VMP), We propose a set of receiver options providing a range of complexity-performance characteristics to adapt to different requirements. Furthermore, we distribute the processing into local processing units (LPU), that can perform most of the complex processing in parallel, before sharing their outcome with a central processing unit (CPU). Our designs are specifically tailored to exploit the spatial non-stationarities and require lower computations than linear receivers such as zero-forcing. Our simulation study, performed with a channel model accounting for the special characteristics of XL-MIMO channels, confirms the superior performance of our proposals compared to the state of the art methods.