Is it permissible to celebrate with family on a permissible occasion, such as success in exams, if it coincides with a blameworthy innovation (bid'ah), such as Christmas, with the intention of celebrating only what is permissible?

If celebrating success necessitates attending a Christmas celebration, then one must avoid this celebration, because it means abandoning the forbidden. If the permissible mixes with the forbidden, then one must abandon the permissible, for safety from the forbidden is not achieved except by abandoning everything, like the mixing of a ritually slaughtered sheep with one that is not.