Because the Talalay and Dunlop processes involve vulcanization at 115+ C to turn the material into a foamed rubber, which denatures the proteins that the immune system recognizes and overreacts to. Denatured protein - think egg white once it's heated and turns white, instead of clear - has its structure radically altered. The molecules get pulled apart, tangled with others, and can in no way be recognized by the antibodies that trigger the immune response.

Similarly, Talalay latex mattress material is usually only about 30% natural and 70% synthetic, and the synthetic does not cause immune response.

If you powder the natural material and directly expose it to IgE, the dominant protein of interest for allergies, you can get a reaction (https://pubmed.ncbi.nlm.nih.gov/10436396/), but in practice with sheets and the outer cloth covering on the mattress basically no proteins ever come into contact with the body. And even in that study only Hev B I was detectable, which is only one of many latex proteins that trigger the immune response, and only 3 of the 21 tested human sera actually had a reaction to the direct mixing with the powdered latex. As far as I understand it, there has never been a confirmed case of an allergic reaction to a latex mattress.