WW1: In 1917, a number of radicals and anarchists, including Emma Goldman, challenged the new draft law in federal court, arguing that it was a direct violation of the Thirteenth Amendment’s prohibition against slavery and involuntary servitude.
WW2: Scattered opposition was encountered especially in the northern cities where African-Americans protested the system. The young Nation of Islam was at the forefront, with many Black Muslims jailed for refusing the draft, and their leader Elijah Muhammed was sentenced to federal prison for inciting draft resistance. Organized draft resistance also developed in the Japanese American internment camps, where groups like the Heart Mountain Fair Play Committee refused to serve unless they and their families were released. 300 Nisei men from eight of the ten War Relocation Authority camps were arrested and stood trial for felony draft evasion; most were sentenced to federal prison.
Vietnam:
But no, no one EVER had a problem with the draft (which is horrifically unethical) until the possibility of women being drafted came up?
Even though the first time that the issue of women being drafted was seriously brought up appears to be in 1981, several men filed lawsuit in the case Rostker v. Goldberg, alleging that the Military Selective Service Act violates the Due Process Clause of the Fifth Amendment by requiring that men only and not also women register with the Selective Service System. And anti-draft protests had been wildly popular multiple times throughout our history before that.