Even in that graph, you see gradual decline in the 70s and 90s, but a fall in union density like falling off a cliff in the 1980s. There is no question that the NLRB was friendlier to organizing in the 1990s-- with good decisions on grad union and temporary worker rights to organize.
But the reality is that basic union law hasn't changed much at all since 1948 Taft-Hartley Act, largely because the GOP has pulled out all stops to filibuster labor law reform. And Dems have typically mobilized to stop any major bad shift in the law. Most of the decline in unions stem from the longterm effects of Taft-Hartley, the changing global economic context, and unions' own failure to invest enough in organizing. Legally they can't do much about T-H, but are making inroads on global organizing, and are slowly improving their investments in organizing, although not quickly enough.
--- Nathan