This is mostly a fair criticism. I've seen the common, 'my body my rights' used in both vaccines and abortion rights. I would point out however, that the vaccine is less deadly, with fewer side effects than carrying a baby to birth. But also, vaccines give herd immunity, which is a direct benefit to the people around you. So they wouldn't be the same.
Vaccines and climate change are not comparable in any way. And just to state, you can be pro-government and anti-government in certain areas of life/society simultaneously without being a hypocrite. Government is and can be expansive and everyone has their limits. Unless you also like pointing out that people live in houses but still go outside?(What is that all about? like come on, you either love living indoors or outdoors you can't do both /s)