We experimentally study the tunability of the cooperativity in coupled spin-cavity systems by changing the magnetic state of the spin system via an external control parameter. As a model system, we use the skyrmion host material Cu2OSeO3 coupled to a microwave cavity resonator. We measure a dispersive coupling between the resonator and magnon modes in different magnetic phases of the material and model our results by using the input-output formalism. Our results show a strong tunability of the normalized coupling rate by magnetic field, allowing us to change the magnon-photon cooperativity from 1 to 60 at the phase boundaries of the skyrmion lattice state.