I suspect that part of the problem is how science is taught in school. Here in the UK, science tends to be about facts and what has been discovered by scientists through the years. It is often far removed from students' daily experiences and relates to little they see in real life.
Perhaps if more attention was paid to the scientific method, teaching students how to verify things by observation, testing and predicting and relating this to stuff in their everyday life, science may become more accessible and better understood.
If children were better educated as to how scientists make discoveries and how their methods and observations are tested, criticised and evaluated by their peers, they may better appreciate how the 'facts' have been arrived at, even if they don't understand how this may affect them directly.
Admittedly, that's a pretty simplistic view, but many of the pupils I work with have no interest in what makes things tick, they just want them to tick.
The key is education and the fact that so many people oppose it from ignorance it must be required in schools from the first grade thru high school. This means the people on the school boards must be educated and support science. If parents won't demand it we must work around them.