Vaccines have a cumulative synergistic effect. The more people that are vaccinated, the more effective they become. Vaccines create a limited supply of antibodies. Your body has a saturation limit of virions that it can handle at any given time. If you are exposed to more virus than the antibodies can handle, then you can still succumb to the disease even if you are vaccinated.
Others not taking the vaccine make our life worse in 2 ways:
1) When people are vaccinated, then they shed fewer infectious viral particles than the unvaccinated. Meaning, if you are vaccinated and you are near a sick unvaccinated person, then you might exceed your limit to fight the disease and get sick. But if you are vaccinated and you are near a sick vaccinated person, then you might NOT exceed your threshold and stay healthy. Ultimately, the more the people that you are around get vaccinated, the less likely you will get sick. We are impacted by those who are not vaccinated because they can overwhelm our vaccine defenses and make us sick.
2) Due to this synergistic effect, vaccines have a critical threshold. Once the population exceeds that threshold, the virus in that area can no longer reliably spread. We just need to cross that threshold and then we can return to normal. People not taking the vaccine are preventing us from returning to normal.
For the reasons above, the more people get vaccinated, the better our vaccines work. The fewer people get vaccines, the worse our vaccines work. If you are anti-mandates, then you are anti-effective vaccines. That has the same end-effect as being anti-vax.
You are basically saying something similar to: you aren't anti-feeding infants but you don't think parents should be forced to feed their infants. The end result is infants die in either case whether you are anti feeding infants or anti forcing parents to feed them. In an ideal world, parents would choose to feed their infants on their own. But, far too many are choosing not to do the right thing.