Certainly SCOTUS maintained a very pro-capital, anti-labor ideology across the board for a very long time, through the Gilded Age and right into the middle of FDR's second term. It wasn't universal. There was some decision or other that Oliver Wendell Holmes dissented from, writing "The Constitution does not enact Marshall's Economics!" But he was writing in the minority. To be sure the entire period from 1860 to 1932 featured a grand total of 2 Democratic Presidents, each holding two terms, one not contiguous--Cleveland and Wilson. Of course it would be wrong in that era to identify "progressive" versus "conservative" with one party or the other; the Republicans were a mixed bag of hard headed business interest types with people holding some fascinating range of idealism. U.S. Grant for instance is claimed as a Georgist, as in Henry George and "Single-Tax." I could also mention Theodore Roosevelt of course. Meanwhile of the two Democrats, Cleveland was infamously a very conservative one, holding to very strict views on the proper power of the Federal government and very tight fiscally, while Wilson, though his administrations featured the passage of a whole raft of Progressive Amendments (senators being elected by popular vote, the Income Tax, and at the end both Prohibition and women's right to vote; also his administration featured the inauguration of the Federal Reserve system and of course the war involved a massive expansion of federal powers and revenues, not all of it reversible) was on the other hand an active reactionary on matters of race and pretty heavy handed with projections of US power abroad, long before entering the Great War as purported crusade for Democracy sending in the Marines to quell democracy in action in places like Nicaragua, Mexico and Haiti.
So I don't think we can attribute the overwhelming consensus of SCOTUS justices as just a political whim of the Presidents, and if we characterize all the Presidents between Lincoln and FDR as "conservatives" then we have to ask why the people kept electing them. On at least one occasion in that time they didn't of course, referring here to the case of Harrison getting in via outright fraud in key state races. Hayes is more infamous as the product of a "stolen election" but in that case I credit the Republicans with stealing it back, the terrorization of African American voters in the South having clearly stolen some of those EV away. I figure one reason so many SCOTUS justices were conservative on labor matters was that the general pool of experienced judges to draw them from was strongly biased in favor of property owners as more authentic and worthy citizens, of greater value to the Republic and impeccable respectability compared to these democratic mobs. By the time FDR was threatening to expand the court to pack it with judges on his side, the pool of judges had had some decades of experience with progressive philosophy. Progressivism (in the sense of the movement in both dominating parties of the later part of the post-Civil War period up to the Depression) could be cynically defined as the effort of elites to preempt elements of the agenda of radical populism, in a top-down managed form acceptable to elites. The People's Party had flexed its muscles in the late 1880s and early '90s and the mainstream two parties scrambled to steal their thunder; also other radical parties, including a succession of worker parties leading up to Deb's leadership of the Socialists, posed the challenge even more sharply that had to be faced with more moderate and elite-controlled concessions. This involved a lot of reforms and things more cynical business politicians called "goo-goo," for "good government" as opposed to machines and so forth. Also regulation of food and medicines in the interest of public safety, a la carte labor reforms, limiting child labor, stuff like that. In that context I suppose that more young up and coming lawyers of the first decade of the century would cut their teeth on advocacy for such reforms, and s the decades passed they got placed on state and Federal benches and eventually the next SCOTUS replacement would be one of these, and more and more of them to choose from. But meanwhile the majority was time-warped back to the verities of their own youth, in which radicals were just plain dangerous and unenlightened and would in their simple minded greed undercut the very foundations of civilization, as they and other respectable people saw it.
Even so, as observed, they didn't quite rule out union organization as plain illegal. (Then again, as I understood it, not long after the Sherman Anti-Trust Act was passed in the late 19th century, aimed plainly at checking corporate consolidation (Quixotically IMHO) the courts struck down all readings to actually use it against business trusts, but affirmed it clearly did ban labor unions, so I think there was a period when unions were all outlaw, no matter how conservative. But clearly this interpretation did not last long!)
The oP question is, what if they did? They'd have to be not just conservative but obtuse to do so IMHO; even the Iron Chancellor Bismarck backed off from keeping either labor unions or the Social Democratic Party in criminal status in Germany--he also set examples of judicious top down state intervention to limit the explosiveness of the working class. And German unions and the SDP were explicitly revolutionary and anti-capitalist! In the USA at least the various radical revolutionaries were offset by conservative unionists like Samuel Gompers's AFL; his patchwork of craft unions would go far to co-opt the most potentially dangerous strata of skilled craft workers and tend to block more than aid comprehensive organization and was quite firmly opposed to the political platform of a mass worker's party to seize control of the state by ballot--still less by other means. So they'd have to be pretty fatuous to be blind to the threat and to the wisdom of having some kind of safety valve. But supposing they were that dumb, then what?
I answered this my way already; are they also dumb enough to attempt to block grassroots populist parties with a radical program of using state power to do what the Court says they can't do in the workplace? If they block unions they seem to be stubborn enough to block that channel too; were I a cynical agent of the propertied classes I would advise tolerating and then regulating and manipulating unions and focus on keeping a radical party off the table instead, but maybe the logic of liberalism would permit the reverse to this OTL pattern more; politics is sacred but the workplace belongs to the boss seems a plain enough interpretation of classic 19th century liberalism. Letting radical parties stand since suppression and manipulation of the vote is a no no would lead to a more radical than OTL electoral ascendency I think, though it might still be quite effectively checked from actions more radical than OTL.
And if they are stubborn enough to firmly try to block both? I subjectively think the odds of a violent revolution, or attempt at it, go way up then--which is why it is foolish for them to be so doctrinaire of course. It might succeed gloriously, or succeed and turn to a nightmare of terror, or fail and usher in an era of more open repression than we've ever seen.
The author asks, well, if worker power just plain fails across the board and workers are driven to abject submission for lower wages, won't the higher profits offset the economic contraction I predicted from that? Well, it matters in whose hands wealth flows. If the worker share of gross production is stunted, that undermines a huge sector of markets that were buoyant OTL. The markets for people like Henry Ford would be constricted, since he aimed at a cheap car for the masses--either he would trim his sails for higher quality and cost in reduced numbers for the rich or simply never crowd into the dozens of competing auto makers. And so across the board; the telephone would not become a common implement in every household since the majority could not afford one (indeed as late as 1932 they were skewed enough to the rich that a major magazine blew predicting the outcome of the election that year, randomly surveying--just people with phones, who were more for Hoover than Roosevelt). The more money finds its way to the workers in the form of wages, the more expansive the US consumer market, which means more jobs for those workers and yet more purchases of big ticket items like refrigerators and washing machines, more megastores like Sears and Montgomery Ward, more consumer credit, etc. The outcome would be the USA would be weaker in situations like WWI and WWII, with recruits less healthy, less familiar with machinery, and probably more alienated into the bargain; a much smaller mass base of savings to tap for wartime credit.
It would be dumb. The question is can we plausibly engineer such dumbness into the SCOTUS with political plausibility?