Hi Ozark Sleeper,
Mattresses mostly use non fire retardant foams (although polyfoam and memory foam are still made with chemicals) and use fire barrier materials to pass the fire regulations. Fire retardant foams are much more common in the furniture industry than in the mattress industry.
Post #4 here and post #2 here has more information about fire barriers and like dn mentioned some of the information on the Strobel site is very misleading.
Post #2 here and the other posts and sources of information it links to also has more information that can help sort through some of the misleading information and claims about a very complex subject (mattress safety) and may help answer the question of “how safe is safe enough for me?”.
While some people choose to go in a DIY direction … it can be quite risky and in some cases much more costly than a component mattress that already has individual layers that can be re-arranged or exchanged. I would read post #15 here before considering this direction. You can also buy a mattress that hasn’t passed the fire regulations (and has no fire retardant) with a prescription and you would also save any tax that was added with a local purchase. Of course you would need to find a smaller manufacturer that would be willing to build a mattress without a fire retardant barrier. One example of a manufacturer that specializes in this is here although there are some people who may prefer a wool quilted cover (that can double as a fire barrier).
Phoenix