It's not quite that though, depending on which crowd you are talking about.

In the realm of medicine, alternative treatments are given credence for this very reason: Steve Jobs tried restricting his diet to fruits and vegetables before turning to chemo and surgery; the shops down the street from my old apartment sell bottles of nutritional supplements--as if a pill of vitamin B12 are any less natural than a pill of aspirin.

In the food world, the discussion is a little different, "synthetic" can mean plants expressing natural, organic {in the chemistry sense} pesticides, artificial sweeteners, lab grown meat, or vanillin produced by yeast. Sometimes the push back is ideological. Sometimes it is justified.

In cosmetics? Well I'm a dirty hippy at heart, so I'm not going to claim anything but ignorance of that whole branch of the world. :)

The heart of what troubles scientists that this language is imprecise. Is a tartrazine allergy any more concerning than a peanut allergy? If I make vanillin in a lab, as long as it's the same chemical, it's safe, right? In the health sense, "chemical," "natural," and "organic" throw out the entire field of toxicology and replace it with language that falls short in so many ways, even if it is more intuitive.

Edit I present you with the most cultural confusing thing I've seen all year: vegan synthetic cheese. This one is getting its own post, actually.