Bridges said he didn't know what his sister's beliefs were but "she's a New Zealander and she should be able to believe whatever she wants".
He said he believed in evolution but that had nothing to do with the issue. He would "absolutely not" talk to his sister about it.
"I'm not going to deign to do something like that on a cheap political hit job."
Mt Hobson Middle School is run by Villa Education Trust, which also has two charter schools.
Alwyn Poole, a Villa Education Trust board member and principal of Mt Hobson Middle School, said Rachel O'Connor was a superb teacher and "very balanced and open in all that she presents".
"The NZ curriculum is broad and designed brilliantly that way by the team that did it. Darwin himself would be very unhappy if the controversies, developments and unfinished business of his theories were not discussed. Everyone who actually knows the basics of science understands that it is built on profound discussion and reaches across broad disciplines. The student's recollection of Mrs O'Connor's statements and the ability to discuss are highly flawed," he said in a statement.
Bridges has pledged to reopen and expand charter schools if National wins the next election.
Villa Education Trust's two charter schools have not yet heard whether Education Minister Chris Hipkins will allow them back into the state school system after the Government said it would get rid of charter schools.