The Montreal Protocol and its amendments (MPA) have been a huge success in preserving the stratospheric ozone layer from being destroyed by unabated chlorofluorocarbon (CFC) emissions. The phaseout of CFCs has not only prevented serious impacts on our health and climate, but also avoided strong alterations of atmospheric circulation patterns. With the Earth system model SOCOLv4, we study the dynamical and climatic impacts of a scenario with unabated CFC emissions by 2100, disentangling radiative and chemical (ozone-mediated) effects of CFCs. In the stratosphere, chemical effects of CFCs (i.e., the resulting ozone loss) are the main drivers of circulation changes, weakening wintertime polar vortices and speeding up the Brewer-Dobson circulation. These dynamical impacts during wintertime are due to low-latitude ozone depletion and the resulting reduction in the Equator-to-pole temperature gradient. Westerly winds in the lower stratosphere strengthen, which is for the Southern Hemisphere (SH) similar to the effects of the Antarctic ozone hole over the second half of the 20th century. Furthermore, the winter and spring stratospheric wind variability increases in the SH, whereas it decreases in summer and fall. This seasonal variation in wind speed in the stratosphere has substantial implications for the major modes of variability in the tropospheric circulation in the scenario without the MPA (No-MPA). We find coherent changes in the troposphere, such as patterns that are reminiscent of negative Southern and Northern Annular modes (SAM and NAM) and North Atlantic Oscillation (NAO) anomalies during seasons with a weakened vortex (winter and spring); the opposite occurs during seasons with strengthened westerlies in the lower stratosphere and troposphere (summer). In the troposphere, radiative heating by CFCs prevails throughout the year, shifting the SAM into a positive phase and canceling out the ozone-induced effects on the NAO, whereas the North Pacific sector shows an increase in the meridional sea-level pressure gradient as both CFC heating and ozone-induced effects reinforce each other there. Furthermore, global warming is amplified by 1.7 K with regionally up to a 12 K increase over eastern Canada and the western Arctic. Our study sheds light on the adverse effects of a non-adherence to the MPA on the global atmospheric circulation, uncovering the roles of the underlying physical mechanisms. In so doing, our study emphasizes the importance of the MPA for Earth's climate to avoid regional amplifications of negative climate impacts.