I get that unions aren't all blue collar manufacturing or transportation and utilities. Those sectors are primarily white labor, particularly in white dominant regions of the country. It took mighty efforts and government intervention to force unions to desegregate, like in police or fireman unions that were essentially white (Italian and Irish) in multiracial cities and regions.
Per your article, 1 out of 10 employee is unionized, and half are in the public sector...that's government which, I assume, includes education and public healthcare. Let's not forget our favorite sample of union labor at work...the DMV. So yes, that's where women and non whites are primarily hired.
But the reality is the brunt of highly paid blue collar union labor is manufacturing, transportation (air, rail, truck, longshore, wharehouse), utilities,.. in sum, mostly men and white based on national demographics. Thanks to the unions, most of these jobs are highly paid (significantly higher than average US income of $64k/year) which puts them at true middle class income of let's say $100k+/year. Their alternative to union work is an instant reduction of 50% or more of their pay package (healthcare, retirement, etc.). No wonder there's a major social schism when non white male and female try to get in those union jobs. The link to Trump and other right wing fringes is strong.
While those sectors are private, they are deeply linked with government, as most of these enterprises have an impact on the functioning of the country and thus represent a potential national security interest. In effect the government has no interest challenging unions because they can easily challenge government.
What is most infuriating though is that We, the Non Union People are on the hook paying high taxes and services to subsidize that labor's high pay packages. For example, why are the US infrastructures falling apart? Because their maintenance cost is exorbitant. Why can't Ford and GM make cars anymore? Because labor costs make them uncompetitive and unions are against efficiencies to reduce their ranks.