According to Daily Mail, oils or oil-based products should never be stored in a skincare fridge as the cooler temperatures can thicken the oil's consistency and spoil the product. Dermatologist Stuart Kaplan told Real Simple, "If your fridge is too cold, certain oils like vitamin C can solidify in the fridge, preventing you from using them altogether." Keeping oil-based serums in a skincare fridge can cause the product to become cloudy and can cause the oils to separate from any water that might be in the product (via The Klog). It's also recommended to keep clay masks out of your fridge. Sullivan told Today that clay masks can change in color or consistency if kept in a fridge. 

Cosmetic chemist Donald Frey told BirchBox that certain emollient products like lotions and conditioners can be destabilized if kept in a fridge and thawed later. The Good Housekeeping Research Institute (GHRI) was generally skeptical of beauty fridges, especially regarding nail polish and perfumes. Dr. Birnur K. Aral, GHRI director of Health, Beauty, and Environmental Sciences said, "With cold temperatures in the fridge, the viscosity of the polish will increase, which might prolong the stability of the polish over time so it doesn't phase-separate." So while you can extend the life on your nail polish, it will thicken and not apply as smoothly.