Science done well is distrustful of its own results. The key is to trust science practiced by trustworthy institutions and individuals and reported on in an accurate and informative way. Similar to good journalism, trust should be earned and verified at every level. Not every time, that isn't reasonable, but enough that you aren't surprised at what you find when you do additional checking. Check sources. Look for conflicts of interest. Survey the field. These are all basic things that people think they do but often don't.

I'll also say that that 'I don't trust science' implies that the scientific method is somehow corrupt. The scientific method is a thing that can be used well or badly. 'I don't trust science' is like saying 'I don't trust statistics'. The wrong person can use out of context science, done well, to imply totally absurd things.