I would be very cautious about using this type of more general information and “translating” it into specific information that would apply to you personally … especially when the driving force behind some of the information you will read about “chemicals” is based on “fear tactics” that are designed to sell some very costly organic mattresses.
The reality is that some people can be sensitive to some of the chemicals that are used to make some types of memory foam (or other foams as well) even though they would be fine with other types of memory foam that don’t use the same chemical formulation. It depends entirely on the individual person and on the specific formulation of the foam. For example if all the people that were sensitive to the naturally occurring chemicals in a tomato wrote about the “symptoms” they experienced when they ate them and someone were to read about hundreds of people that had negative reactions when they ate them then it would probably be enough to stop them from ever eating tomatoes again even though the odds would be very low that what they are reading would apply to them.
The question of “how safe is safe enough for me” is specific to each person and their individual sensitivities, health concerns, circumstances, criteria, beliefs, and lifestyle choices (just like some people may choose an organic or even a vegan diet and would consider other diets to be “unsafe”) but there is more information in post #2 here and the more detailed posts and information it links to about safe, natural, organic, “chemical free”, and “green” mattresses and mattress materials that can help you sort through some of the marketing information and terminology that you will encounter in the industry and can help you differentiate between them and answer “how safe is safe enough for me” or “how natural is natural enough for me” so you can decide on the types of materials you are most comfortable having in your mattress. This way you can focus on the materials in a mattress and the certifications that it has rather than the name of a manufacturer that makes it. These types of issues can be complex and again are generally specific to each person and their individual sensitivities, health concerns, circumstances, criteria, beliefs, and lifestyle choices.
Whether you are sensitive to any particular material or any of the chemicals inside it or whether it could affect any medical condition you may have is also really a health question that can’t be answered specifically and would be a question that you would need to discuss with a health care practitioner that that you trust and that is familiar with any particular health conditions that you may have. Even something like caffeine or other stimulants can aggravate irregular heartbeats and for some people should be completely avoided.
Outside of this … the only reliable way to assess the “safety” of any particular material is based on the certifications it has for harmful substances and VOC’s (you can read more about certifications in post #2 here) but it’s still possible that even with a certification a particular person may have a specific sensitivity to certain materials that for most people would be fine (even if they had an irregular heartbeat). In very general terms and based only on anecdotal information and “reports” you will find that memory foam will have the highest incidence of people that have complaints about symptoms they they experience when they sleep on memory foam followed by polyfoam followed by latex.
The Brooklyn Bedding BestMattressEver doesn’t contain any memory foam and only contains latex and polyfoam. The latex is certified by OekoTex and the polyfoam is certified by CertiPUR so for the very large majority of people these materials would certainly be “safe enough”.
The Casper mattress does have a 1.5" gel memory foam layer in addition to the 1.5" layer of latex and the polyfoam but their memory foam and polyfoam is also CertiPUR certified and their latex is also Oeko-Tex certified so for most people “safety” also wouldn’t be an issue or concern with a Casper mattress.
There is also more information about the “simplified choice” category of mattresses (including Casper and Brooklyn Bedding’s BestMattressEver) in this topic that may help you make more meaningful quality/value comparisons between them as well.