So is the Republican party still the party of activist government, labor rights, conservation, and business regulation?
The old GOP had both conservative and progressive wings. Also remember that in 1936 FDR wouldn't shake hands with Jesse Owens, while Alf Landon was a good friend of his.
Until 1896 the two parties were very similar, and after that both parties had battles between progressives and conservatives at every convention until after the New Deal when Republicans were overwhelmingly conservative and Democrats overwhelmingly liberal.