We study the Casimir interaction between two dielectric spheres immersed in a salted solution at distances larger than the Debye screening length. The long distance behavior is dominated by the nonscreened interaction due to low-frequency transverse magnetic thermal fluctuations. It shows universality properties in its dependence on geometric dimensions and independence of dielectric functions of the particles, with these properties related to approximate conformal invariance. The universal interaction overtakes nonuniversal contributions at distances of the order of or larger than 0.1 μm, with a magnitude of the order of the thermal scale k_{B}T such as to make it important for the modeling of colloids and biological interfaces.