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The assembly and co-evolution of supermassive black holes (SMBH) and their host galaxy stellar population is a key open questions in galaxy evolution. Stellar mass ($M_\star$) and star formation rate (SFR), are inferred by modeling the spectral energy distribution (SED). For galaxies triggering SMBH activity, the active galactic nucleus (AGN) contaminates the light at all wavelengths, hampering the inference of galaxy parameters. Incomplete AGN templates can lead to systematic overestimates of the stellar mass, biasing our understanding of AGN-galaxy co-evolution. This challenge has gained further impetus with the advent of sensitive wide-area surveys with millions of luminous AGN, including by eROSITA, Euclid and LSST. We aim to estimate the accuracy and bias of AGN host galaxy parameters and improve upon existing techniques. This work makes two contributions: 1) a new SED fitting code, GRAHSP, with a flexible, empirically motivated AGN model including a power law continuum emission lines, a FeII forest and a flexible infrared torus. We verify that our model reproduces published X-ray to infrared SEDs of AGN to better than 20\% accuracy. A fully Bayesian fit with nested sampling includes uncertainties in the model and the data, making the inference highly robust. 2) we created a benchmark photometric dataset where pure quasars are merged with non-AGN pure galaxies into a hybrid (Chimera) object but with known galaxy and AGN properties. Comparing the true and retrieved $M_\star$, SFR and AGN luminosities shows that previous codes systematically over-estimate $M_\star$ and SFR by 0.5 dex with a wide scatter of 0.7 dex, at AGN luminosities above 10^44 erg/s. In contrast, GRAHSP shows no bias on $M_\star$ and SFR. GRAHSP also estimates more realistic uncertainties. GRAHSP enables characterization of the environmental conditions conducive to black hole growth. (abridged), Comment: accepted in A&A