Yes, there indeed a phobia for the irrational fear in which you are describing. It is called Chemophobia, and it is described as
Chemophobia is specifically a distrust of what people view as
"artificial" chemicals – food additives, drugs, pesticides and so on.
This is usually attributed to a lack of trust and knowledge among the
public, which is often fueled by tabloid-based health scares and the
occasional additive shown to possibly be toxic. Advances in the field
of analytical chemistry are also thought to be behind chemophobia, as
modern techniques are capable of identifying substances in very low
(parts per billion or even trillion) and harmless quantities.
For a more substantiated and scholarly source, have a look at Food Chemistry and Chemophobia. For just a brief glimpse of what the detailed article is about, here is the abstract below:
Chemophobia is the exaggerated fear of anything ‘chemical’ which is
found quite widespread both in the Western world and in Asia. That
food incontrovertibly is chemistry seems to require regulation of all
sorts. As we will see below, that would truly necessitate gargantuan
determination exceeding every regulatory effort to date. Worse, it
will be futile. Our food is peppered with natural compounds such as
organohalogens, dioxins, aflatoxins, and many others. These we will
briefly discuss, including their natural whereabouts. Overall, the aim
of this paper is to show that food is chemistry beyond our immediate
control, including those synthetic chemicals that are deemed to be
artificial and should not be found in ‘safe’ food. The latter is an
overestimation of regulatory competence and an underestimation of
nature to produce most unlikely chemicals in unlikely places,
including our food.
Ta Da! There is basically a phobia for everything.