I'd say that a more charitable reading of the argument "it's not political" is that it isn't political issue in the US sense of an issue that falls neatly into republican/democrat camps. I think you will find people of different political leanings on all sides of the vaccine issue. I think of myself as moderately left wing but find myself aligning more with you and @Zefah, TheDreadBaron etc etc on this issue because I feel an intuitive revulsion to pushing medical treatments on people and am (like you) not very trusting when it comes to the information we're getting out of government and (especially) big pharma.
It is hard everywhere to assign things as political or not. Especially since opposition seldom wants to agree with current government.
If there is anyone that wants tight control (and masks etc.) here in Sweden it is the right wing.
Seems to be a big no to vaccinating kids needlessly and forcing vaccinations on anyone at least from all parties.