First, unreproducable science isn't science.
Incorrect. Sometimes it is not possible to reproduce results in any meaningful way, but it is still considered science. For example, how could you reproduce the results of climate change? Build another earth and wait a few hundred/thousand/million/billion years for the result? There are many other areas, such as medicine, social sciences and theoretical physics where reproducing results is simply impossible (e.g. you can't make people younger and cancer free, then reproduce their exact lifestyle for 30 years to see if cigarettes gave them cancer).
That's the reason why the Republicans want this. They can defeat any science they don't like by simply claiming that it can't be reproduced, and prevent the EPA using it to make rulings. It's specifically targeted at the EPA, which deals with environmental and health issues that are often hard to prove beyond any reasonable doubt in the first place, without the extra requirement of having to poison people just to see if they get sick again or if it was some unrelated illness.