What did freedom and equality mean to workers in the US's new industrial economy during the mid 1870s?
Freedom and equality meant very little to workers in the early Industrial age. Workers were often treated as numbers, were forced to work long hours under dangerous conditions, and could be fired for the slightest reason. They received no protection from the government or the courts; in fact the government frequently sided with the factory owners. When Eugene V. Debs, a union organizer, led a strike against the railroads after the railroads lowered wages, President Grover Cleveland had mail cars attached to the rear of all trains, so that any worker refusing to operate the trains was interfering with the mails. The attorney general obtained an injunction ordering the workers to return to work, and Debs was sent to jail for violating the injunction. The court said in its order (In re Debs),
The strong arm of the Federal government may be put forth to brush away all obstructions to the freedom of interstate commerce or the transportation of the mails.
Any mention of the workers rights is conspicuous by its absence. Even more troubling, in 1886 in Santa Clara County vs. Union Pacific Railroad, the court held that corporations were "persons" for legal purposes and therefore entitled to protection under the 14th Amendment. Again, no mention of workers' plight.
Much of this was because labor movements were associated with anarchism. By the same token, factory owners had powerful political connections; so to answer your question, the freedom and equality for workers at this time was practically nonexistent.