Over the course of the period between the founding of the Republican Party by anti-slavery activists in 1854 and Richard Nixon's Southern Strategy in 1968, the Republican Party evolved in a number of ways, and along with the obvious (civil rights) the party line has evolved and refined its focus on labor issues. I can't speak much to the general view of Republicans regarding labor prior to the 20th century, but at least on Teddy Roosevelt's part, he was sympathetic to labor throughout his political career, including as Governor of New York and as Vice President. He wasn't alone in this either. Progressive Republicans were a thing at the time.

However, I don't think it is fair to say that Teddy Roosevelt simply favored labor over corporations without adding the qualifier "in the context of his time." Teddy Roosevelt was all about the "square deal" which was his proposal to protect Americans, consumers and labor alike, as well as the environment from some of the worst abuses of unchecked industrialization. Teddy Roosevelt's policies were essentially a reaction to the very unbalanced conditions of the so called Gilded Age, when powerful corporations, many of them monopolies, held disproportionate market power over both their consumers and their labor supply. In this context, Teddy Roosevelt's policies were intended to give labor a more fair deal, and not a sweet deal. It should also be noted that TR, was in many ways an outlier as far as politicians go. He had his own ideas and really stood up for and stood firm behind his convictions. He had joined the Republican Party back in 1880, only 15 years after a controversially progressive Republican President (the first Republican President) had led the United States to victory in a brutal civil war over slavery. It isn't hard to see how the Republican Party of the day may have been attractive to a high-minded idealistic young man with ambitions to bring about further progress of his own.

The labor-friendly Republicans started becoming more rare after TR's presidency, and became almost non-existent as the Republican party became more and more preoccupied with anti-communism over the following decades into the 50's and 60's (as socialism and communism was strongly associated with organized labor).

As a Democrat, FDR's pro-labor policies need a lot less explaining. Democrats were not universally pro-labor, but definitely more so than their GOP opponents were generally. However, FDR, while in favor of collective bargaining in the private sector was not in favor of collective bargaining in the public sector.