The question specifies "civil rights" as opposed to "human rights," so the answer that follows will presume that the student is interested in issues of racial and gender equality rather than the broader issue of universal human rights that was the principle concern of the 1948 Universal Declaration of Human Rights. The latter issue, however, will also be discussed briefly.
The United States Army was a formally segregated institution, representative of the society it protected. The civil rights movement in the United States would not begin to witness substantive legal victories for a number of years -- the 1954 Supreme Court ruling in Brown v. Board of Education would represent the first major breakthrough in desegregation -- and African American soldiers and sailors were kept subordinate to their white counterparts and prevented from opportunities for advancement and even from being able to participate directly in the fighting in Europe and Asia until very late in the war. The fundamental injustice of a system that continued to discriminate on the basis of ethnicity or race became even more apparent when those African American soldiers were finally permitted to enter the fight against fascism and performed well above the expectations of a racist white-dominated society. The battlefield successes of all-black units as well as the exemplary record of the so-called Tuskegee Airmen, black fighter pilots who were kept in segregated units but performed brilliantly when allowed to fight, illuminated the irrationality of racial segregation.
It would take another several years following the end of World War II, but President Harry S. Truman finally officially desegregated the U.S. Armed Forces in 1948. His issuance of Executive Order 9981 in July of that year began with an expression of the obvious regarding the incongruity of a democratic nation imposing undemocratic constraints on a segment of its population:
"WHEREAS it is essential that there be maintained in the armed services of the United States the highest standards of democracy, with equality of treatment and opportunity for all those who serve in our country's defense..."
The experiences of World War II, then, heavily influenced many Americans' perceptions of civil rights, but many other Americans, especially across the South, remained implacable foes of desegregation. In that sense, the experience of the war did not have as far-reaching implications for civil rights as many had hoped would be the case.
Gender roles similarly were only marginally affected by the war. While hundreds of thousands of women went to work in the nation's burgeoning armaments industries vital to the war effort, and while thousands more served valiantly as nurses in and near combat zones, women's rights were not substantially advanced by these developments. On the contrary, women's rights would continue to be a major issue for decades to come.
With respect to human rights issues in Western Europe, the atrocities associated with World War II, especially the Holocaust, resulted in a greatly enhanced role for such rights in the post-war environment. The horrors of the Nazi extermination of millions of Jews, Roma, homosexuals, disabled Germans, and others compelled post-war West European politicians to fundamentally reconsider the importance of establishing more enlightened policies with respect to discrimination. The resulting emphasis on human rights resulted in the aforementioned Universal Declaration of Human Rights adopted by the newly-created United Nations in 1948. That landmark document, a link to which is provided below, set forth a series of principles that would be expected to provide a legal framework for all nations with respect to nondiscrimination and the universal application of fundamental rights like freedom of religion and expression. In this sense, the war's carnage and the enormous scale of suffering resulting from Germany's racial policies heavily influenced Western Europe's subsequent approach to human rights.