Is it true that glycerin prevents remineralization of your teeth?

This is not true. This appears to be a claim started by a chemist who wrote an article without much evidence to support the claim and the information spread. In fact, this claim goes against the basic chemistry of glycerin.
Glycerin is water-soluble. It dissolves easily in water and it is also bacteriostatic meaning it helps prevent bacteria from forming. Because glycerin dissolved easily in water, when you use toothpaste and rinse your mouth after brushing (or simply take a drink of water later in the day) the glycerin will easily be removed from your teeth.
We use organic glycerin in our toothpastes (sourced from mustard seeds, not soy or palm) because it's a natural emulsifier, it helps mix our oil and water-based ingredients. It's what helps makes our paste a paste and is a pretty important ingredient. Glycerin also acts as a natural sweeter without contributing to tooth decay.