The biophysical basis for the ability of animals to detect the geomagnetic field and to use it for finding directions remains a mystery of sensory biology. One much debated hypothesis suggests that an ensemble of specialized light-induced radical pair reactions can provide the primary signal for a magnetic compass sensor. The question arises what features of such a radical pair ensemble could be optimized by evolution so as to improve the detection of the direction of weak magnetic fields. Here, we focus on the overlooked aspect of the noise arising from inhomogeneity of copies of biomolecules in a realistic biological environment. Such inhomogeneity leads to variations of the radical pair parameters, thereby deteriorating the signal arising from an ensemble and providing a source of noise. We investigate the effect of variations in hyperfine interactions between different copies of simple radical pairs on the directional response of a compass system. We find that the choice of radical pair parameters greatly influences how strongly the directional response of an ensemble is affected by inhomogeneity.