  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)
