Because her alternative could be used as a technicality in court to invalidate marriage licenses. According to the law the name of the person holding her office has to be on the marriage certificate for it to be valid. If you dont think someone would sue to invalidate those marriages on that basis you are naive.
People objected on religious grounds interracial marriage, desegregation, women/blacks voting and ending slavery too. 50 years from now we will remember this in the same vain as those issues. What side of that do you want to be on?
“Almighty God created the races white, black, yellow, malay and red, and he placed them on separate continents. And but for the interference with his arrangement there would be no cause for such marriages. The fact that he separated the races shows that he did not intend for the races to mix.”
— Judge Leon M. Bazile, January 6, 1959