Hi Stella.
The only reliable way to assess the “safety” of different materials in more general terms is based on lab tests and the certifications they have for harmful substances and VOCs (regardless of whether they are organic or natural or synthetic) so that you have some assurance than the VOCs are below the testing limits for the certification. If the materials in a mattress or the mattress itself has a reliable “safety” certification then for most people they would certainly be “safe enough” … regardless of the type of material or the name of the manufacturer on the label.
There is more about the different types of organic and safety certifications such as Oeko-tex, Eco-Institut, Greenguard Gold, C2C, and CertiPUR-US in post #2 here and more about some of the differences between organic and safety certifications in post #2 here and there are also some comments in post #42 here that can help you decide whether an organic certification is important to you for environmental, social, or personal reasons or whether a “safety” certification is enough.
CertiPur* tests for harmful substances and VOC’s in the polyfoam and memory foam used in mattresses. They have a list of mattress manufacturers here* which are certified and the foam producers that are certified are listed here*. You can see what they test for here**.
**Always check CertiPur site for the latest guidelines available
Phoenix