It is my understanding that individuals who have been excommunicated and restored to full fellowship cannot hold positions as a bishop, seminary instructor, or temple worker. Why is that the case?
Your impression is not entirely unfounded. But it is not quite accurate.
First take a look at my previous post on the restoration of temple blessings:
After a look through the Encyclopedia of Mormonism under the topics of Excommunication, Bishops, Callings, Seminaries, and several topics including “Temple”, nothing is to be found regarding the restriction of certain callings.
What is found is that certain rights, blessings, and positions are withheld until “The ordinance of restoration of temple blessings (is) authorized only by the First Presidency.” (EM; “Disciplinary Procedures”).
Priesthood offices restored are only to Priest (for an adult) Elder, or High Priest. Other priesthood offices that usually come by virtue of position (e.g.bishop or patriarch) are not immediately restored. But there is no statement in public documents that state they will never be restored.
The most famous example was the restoration of Orson Pratt in early Church history. He was an apostle, then excommunicated, then after re-baptism and restoration of blessings he was called to the position of apostle again. But that doesn’t necessarily mean that is the current policy.
Apart from that, I find no reference to any other restrictions on callings such as seminary teacher or temple worker. That is not to say that some bishops or stake presidents may not make a judgment on the matter and place such restrictions on some individuals or positions. And it is entirely possible there is a common practice that is not written in available documents. But I haven’t been able to find an official source that states it in any publicly available documents.