If both students have special needs, the school district must accomodate both, but they cannot accomodate one (such as the child with severe allergies) at the expense of the other (such as a child who needs his/her service dog). While the school district would prefer to make life easy by saying "no service dog", that's not what they are required to do. They must create an appropriate learning environment for each child.
If a child's allergies are so severe that he/she cannot tolerate animal dander in any form, the service dog would not be the only issue because the odds are that many of the child's classmates will be carrying animal dander on their clothing. The school district would have to create a safe learning environment for the child with allergies, whether it's a separate classroom or a change in placement or some other accomodation, with or without the presence of a service dog. They can't just tell the rest of the students to get rid of their pets. A look at the research that's been done on the issues surrounding service dogs in classrooms & at anecdotal evidence shows that the allergy issue is not the problem in real life that it tends to be in conjecture.