I have children who are allergic. I read the ingredients very carefully.
Personally, I avoid non-kosher at the same level. When I see a hechser, it is a starting point then I look at the ingredients.
Consider Kedem grape juice. A nice chassidish hechsher – but product contains potassium metabisulfite so children get one cup at each shabbos meal – no more. (There are brands of grape juice that do not have any sulfites.)