In this study, various cellulose derivatives were tested with various preservatives to see which ones retained their efficacy. Here's the list...
Methylcellulose reduced paraben efficacy.
Methylcellulose, sodium carboxymethylcellulose, and hydroxypropylmethylcellulose all reduced phenoxyethanol efficacy.
Gelatin reduced paraben efficacy.
Polyvinylpyrrolidone (PVP) reduced paraben efficacy.
A few naturally occurring thickeners work by protecting the bacterial cells in our creations so the paraben preservatives can't attack the beasties. These include acacia gum, tragacanth, sodium alginate, guar gum, and carageenan.
So what does this all mean? If you're using any of these ingredients, consider your preservatives wisely.