The rational basis test traditionally doesn't require that you use the best method, or all methods better than the one you're using, or that you can prove that your method works; you need merely show that it can be reasonably believed that your method has an effect that would serve a legitimate end. And you don't even have to show the end was what actually motivated the action in the first place, just that the action can serve the end.

It's a very easy test, which is why the assertion by the judge that it wasn't met is either going to have very wide consequences, or get overturned.

The judge's decision is much more strongly defensible on, say, the grounds that gender is a quasi-suspect class under the law, and that intermediate scrutiny (much more rigorous than rational basis) applies to the question of whether women but not men can be prohibited from marrying women.