In this article we perform ab initio calculations in order to assess the reactivity of ultracold RbSr ($^2Sigma^+$) $+$ RbSr ($^2Sigma^+$) collisions occurring on the singlet as well as the triplet potential. At ultracold energies reactions are energetically possible if they release energy, i.e., they are exoergic. The exoergicity of reactions between RbSr molecules producing diatomic molecules are known experimentally. We extend this to reactions producing triatomic molecules by calculating the binding energy of the triatomic reaction products. We find that, in addition to the formation of Rb$_2$ and Rb$_2$+Sr$_2$ in singlet collisions, also the formation of Sr$_2$Rb and Rb$_2$Sr molecules in both singlet and triplet collisions is exoergic. Hence, the formation of these reaction products is energetically possible in ultracold collisions. For all exoergic reactions the exoergicity is larger than 1000 cm$^{-1}$. We also find barrierless qualitative reaction paths leading to the formation of the Rb$_2$Sr, Sr$_2$Rb, and singlet Rb$_2$ reaction products. These reaction paths imply the existence of a qualitative reaction path with a submerged barrier for the creation of the singlet Rb$_2$+Sr$_2$ reaction product. Because of the existence of these reactions we expect ultracold RbSr collisions to result in almost universal loss even on the triplet potential. Our results can be contrasted with collisions between alkali diatoms, where the formation of triatomic reaction products is endoergic, and with collisions between ultracold SrF molecules, where during triplet collisions only the spin-forbidden formation of singlet SrF$_2$ is allowed.
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