**Q:** <sub>[as originally formulated by the OP]</sub> *Why is topos theory not taken seriously?*     

The way this question is phrased seems too subjective, but I may point out that topos theory has been suggested as an alternative mathematical structure with which to formulate quantum theory. See the <A HREF="https://ncatlab.org/nlab/show/Bohr+topos">Bohr topos</A> entry in nLab. It is not mainstream, but it is a serious development in the context of quantum logic.