I'd like to see some documentation on this one. My understanding is that most of the eugenics laws were bipartisan, promoted by "progressives" of both parties, before "progressivism" became entirely or even mostly associated with the Democratic Party.
The same way various things are today labeled, "bipartisan" when three RINOs in the House vote with the democrat majority? States with eugenics laws all had state legislatures with large democrat majorities. If you want to say that there were "progressive Republicans" who went along you're probably right but that doesn't make it a true "bipartisan" effort by any means.
There were, indeed, some prominent Republicans who supported such initiatives, some even wanting them enacted on a national level. Most of those advocating such laws were very wealthy and very much opposed to allowing continued immigration from Eastern and Southern Europe in spite of the fact that they preferred to employ them rather than non-immgrants in their mines and factories. That some the same wealthy individuals supported a good many things the Republican party would never adopt as a part of their platform pretty well shows what sort of "Republicans" those folks were just like you now find nominal Republicans who are, in fact, nothing of the sort.