If that were the case then the church could go around shooting all D-Classes without any consequence (except for Uglyhood).
It could be something like it negates the powers of the alien parasites, but still, Sera didn't even directly hit her. Elsa just withstood it because she's that much of a badass regardless.
Going to say that the gun can also kill humans as Sera said if Elsa wasn't Uglyhood, then she would be committing murder. The gun can kill humans, but can also kill aliens - usually, guns can't damage aliens.