And not getting the vaccine is potentially bad for you, and those around you, much more so than it is bad for anyone you're protesting against.
The vaccine helps your body fight the virus, and reduce the spread of the virus in your local community. That should be the key point in deciding if you get a vaccine.
Assuming a disagreement about reality is a disagreement about values is a great way to straw man without knowing it.
I was 100% on board with at home testing every 3 days schemes, mask wearing (even though I doubt the efficacy of most masks), but having compulsory medical procedures with a relatively untested, proprietary technology is where I draw the line.
I can accept the argument "this is where I draw the line" if and only if in pre-Covid you would have refused most of what doctors would prescribe you. If you want to draw a line between pre-Covid modern prescription drugs (all proprietary, many also with weird new tech, all tested on far less people than the vaccines) and the current vaccines, you're going to need a substantially different argument than "medical procedures with a relatively untested, proprietary technology". Heck, even simply saying "I don't believe that such procedures should be compulsory ever for any reason" would be a much more reasonable argument than that.
It's intellectually dishonest to chop up what he says, even though you admit it, to make it easier to argue against.
You aren't 'punishing' those in power by not taking the vaccine. You are punishing every other person in society.