Preservatives achieve their intended function by broadly destroying and preventing the growth of microbes, which are an integral part of our digestive system. So I would flip the question: what evidence is there that preservatives don't damage a healthy human microbiome?
Here is a review of some of the research. It seems to still be an open question because of the many variables involved: https://pmc.ncbi.nlm.nih.gov/articles/PMC9864936/