The cosmic dipole measured in surveys of cosmologically distant sources consistently diverges from the expectation set by the Cosmic Microwave Background (CMB), posing a serious challenge to the Cosmological Principle and the standard model of cosmology. These inferences rely on our understanding of the source counts and underlying systematics. For many systematics, it is not generally possible to write down the analytical likelihood. Here, simulation-based inference (SBI) is a powerful tool that enables Bayesian inference when the likelihood is intractable. We present a flexible SBI framework that quantifies the cosmic dipole tension using neural ratio estimation. We show that the recovered tensions between Planck, NVSS, RACS and CatWISE are comparable to those in the literature. These may be extended with any number of systematics, setting the stage for the future. If we are to resolve the anomaly or strengthen the challenge against ΛCDM, modelling and quantifying systematics to rule them out as culprits of tension will be essential as we enter the SKA-LSST era.