It is well known that giant planets open deep gaps in their natal gaseous protoplanetary discs. However, it is unclear how gas accretion onto growing planets influences the shape and depth of their growing gaps. We perform isothermal hydrodynamical simulations with the Fargo-2D1D code in which planets accrete gas within full discs that range from 0.1 to 260 AU. The gas accretion routine uses a sink cell approach, where we use different accretion rates to cope with the large span of gas accretion rates in the literature. We find that the planetary gas accretion rate increases for larger disc aspect ratios and larger viscosities. Our main result shows that gas accretion has an important impact on the gap opening mass: we find that when the disc responds slowly to a change in planetary mass (i.e. at low viscosity), the gap opening mass scales with the planetary accretion rate, with a higher gas accretion rate resulting in a larger gap opening mass. On the other hand, if the disc response time is short (i.e. at high viscosity), then gas accretion helps the planet carve a deep gap. As a consequence higher planetary gas accretion rates result in smaller gap opening masses. Our results have important implications for the derivation of planet masses from disc observations: depending on the planetary gas accretion rate, the derived masses from ALMA observations might be off by up to a factor 2. We discuss the consequence of the change of the gap opening mass on the evolution of planetary systems by taking the example of the Grand Tack scenario. Planetary gas accretion also impacts the stellar gas accretion, where we find only a small influence due to the presence of a gas accreting planet.