There were anti-eugenics movements, yes. The Catholics were extremely anti-eugenic for the most part, because it involved a lot of things they saw as contrary to doctrine (control of reproduction obviously being at the center of it). There were also strong negative reactions to certain forms of eugenics, like euthanasia, which were crystallized in several major controversies (e.g. Dr. Harry Haiselden's refusal to treat "defective" babies).
There were also push-backs from scientists who thought that the self-proclaimed eugenicists were often frauds, charlatans, and racists. These scientists were not necessarily against all forms of eugenics, but were often against things like compulsory sterilization (which the Hardy-Weinberg principle makes clear would not likely affect the gene pool meaningfully, unless carriers were also sterilized), immigration restriction on "eugenical" basis (Franz Boas argued strongly against this), and against the most vulgar forms of eugenic racism (e.g. Madison Grant's Nordic typology). "Eugenics" is a very broad category, and there were many who believed it was important but would never have supported coercive tactics.
The Great Depression took a lot of the air out of the American eugenics movement because it became clear that poverty and criminality were probably more situational than essential. There was even an anti-sterilization movie made in 1934, though it wasn't very popular as far as I can tell.
As an aside, the term "eugenics" did not become completely tainted until the 1960s and 1970s, well after the Holocaust. Many US states continued sterilizing the "unfit" for eugenic justifications well into the 1960s. It was not an overnight change. Diane Paul's Controlling Human Heredity is my favorite short book on the history of eugenics by a careful historian (there is a lot of bad, sensationalistic history on this topic out there).
Outside of my area of historical expertise, but the biggest example that comes to mind is actually in Germany; Action T4 was the pre-wartime Nazi eugenics program (which continued in various forms into the war), focused entirely on sterilization and execution of Germans with disabilities. I'm dramatically simplifying, but by 1940, the objections on the part of the Church, medical establishment, judiciary and public had become extraordinarily robust. There were widespread protests, particularly among Catholics thanks in part to a widely-disseminated sermon by the Biship of Munster denouncing the program, and especially after it became generally believed that injured German soldiers from the Russian front were going to be euthanized under the program.
Hitler actually shut the program down in 1941 to placate the Church, the public, and also members of his own bureaucracy who objected (though the latter were also removed from power relatively quickly). Many of the personnel involved were transferred into the units that authored plans for the Final Solution.
Source: Robert Jay Lifton, Medical Killing and the Psychology of Genocide
Had to get to this one briefly before bed:
I can speak roughly to the American case: there were anti-eugenicists, but much less anti-eugenics. Theorists like Ross and Stoddard were among a popular and intellectual wave of scholars and bureaucrats who consolidated eugenics as a reaction to empire and the Rising Tide of Color, and ultimately got their way with anti-immigration laws.
But eugenics from the top opposed communism and the International Workers of the World. But these labor movements publicly opposed theorists from the top and launched campaigns to associate the hobo/tramp/destitute working class with masculinity and virility--suitable for a eugenics project. Feminists like Gilman opposed patriarchal eugenicists, but adopted ideas of biological eugenics. And even when the IWW sought to include black folks...they still used eugenics to show how black men conformed to certain masculinities that, while imperfect to the worker's cause because of implicit racial inferiority, still served some strong purpose to the movement.
Source: Daniel E Bender, American Abyss