Context. Isotope abundance ratios provide a powerful tool for tracing stellar nucleosynthesis, evaluating the composition of stellar ejecta, and constraining the chemical evolution of the Milky Way. Aims. We aim to measure the 12C/13C, 32S/34S, 32S/33S, 32S/36S, 34S/33S, 34S/36S, and 33S/36S isotope ratios across the Milky Way. Methods. With the IRAM 30 meter telescope, we performed observations of the J = 2-1 transitions of CS, C33S, C34S, C36S, 13CS, 13C33S, and 13C34S as well as the J = 3-2 transitions of C33S, C34S, C36S, and 13CS toward a large sample of 110 high-mass star-forming regions. Results. We measured the 12C/13C, 32S/34S, 32S/33S, 32S/36S, 34S/33S, 34S/36S, and 33S/36S abundance ratios with rare isotopologs of CS, thus avoiding significant saturation effects. With accurate distances obtained from parallax data, we confirm previously identified 12C/13C and 32S/34S gradients as a function of galactocentric distance. In the central molecular zone, 12C/13C ratios are higher than suggested by a linear fit to the disk values as a function of galactocentric radius. While 32S/34S ratios near the Galactic center and in the inner disk are similar, this is not the case for 12C/13C, when comparing central values with those near galactocentric radii of 5 kpc. As was already known, there is no 34S/33S gradient but the average ratio of 4.35 ± 0.44 derived from the J = 2-1 transition lines of C34S and C33S is well below previously reported values. A comparison between solar and local interstellar 32S/34S and 34S/33S ratios suggests that the Solar System may have been formed from gas with a particularly high 34S abundance. For the first time, we report positive gradients of 32S/33S, 34S/36S, 33S/36S, and 32S/36S in our Galaxy. The predicted 12C/13C ratios from the latest Galactic chemical-evolution models are in good agreement with our results. While 32S/34S and 32S/36S ratios show larger differences at larger galactocentric distances, 32S/33S ratios show an offset across the entire inner 12 kpc of the Milky Way.