Start by looking at
The US Food and Drug Department consumer page. This
FDA link (while old) does list the steps that need to be taken before adding a preservative to food:
1) Manufacturer must prove it is safe in the amounts consumed.
2) Manufacturer must prove any chemical the preservative breaks down to it is safe in the amounts consumed.
3) Manufacturer must prove the cumulative effect of the preservative in the body is safe.
4) Manufacturer must prove the toxicity is minimal (including possible cancer links).
5) The preservative must be used in minimal quantities - no more than is absolutely necessary.
6) Any new data on a preservative requires steps #1 - #5 to be reevaluated.
Thus with CURRENT scientific knowledge, preservatives are safe. But we don't currently know everything. New data can come along and show that a preservative that was thought to be safe might in fact be harmful in some rare cases.
It is the thought that maybe current science knowledge is wrong that makes people want to avoid preservatives. Many countries have populations that are horribly terrified of preservatives, the US seems to tollerate them. I personally see people eating preservatives all the time without consequence. So I trust current scientific knowledge that they are safe to eat (even when considering the cumulative effect).