Posteriors estimated from a fiducial XOD for different conditioning of NPE. The XOD is produced from a 200 deg² X-ray survey, selecting clusters with the flux cut CR_lim = 0.02 c/s. In plain blue we show a posterior marginalised on the feedback parameters, while in dashed blue we show a posterior from an NPE only conditioned on the cosmology. The vertical and horizontal lines recall the fiducial values used for generating the tested XOD.