What a great question, and I will be tackling the American Expeditionary Force of 1917-1918.

Unlike African Americans, other races and ethnicities were not segregated in the American Expeditionary Force. Whether one was Chinese, Mexican, Indigenous, Jewish, or any other group, these men were, for the most part, sent to the same units as white men. Black men were relegated to black units, although often these would have white officers (and there were no black commissioned officers above junior officer ranks such as Lieutenant).

There are a few things to keep in mind before we really dig into this subject: First, is that men who were natural born citizens, declarant alien residents (that is, declared their intention to become a citizen), and even non-declarant aliens were drafted (albeit, non-declarant men were not supposed to be, but a large percentage made it through). Approximately 1/5th of the AEF were not citizens, and many more immigrants.

However, because of how the draft operated, while men were not necessarily lumped together on a say, town to town basis, there was often a regional grouping to the initial composition of regiments and divisions created through the draft. Think of these units as being very generally regional, such as for the Midwest or Southwest. In effect, this meant that often (at least initially) many ethnic groups and other races were often in the same regiment and companies. This regional character diluted over the course of the war, and even when it was at its strongest, you would still see men from around the country in the those units. Because of this (at least initial) regional bias in the creation of draftee units, minority men were often placed into regional units, rather than those from further afield. Tejanos (citizen and non-citizen Mexican residents of Texas), for instance, were mostly grouped within the various units of the 36th, 40th, and 90th Divisions because of this. Asian Americans living in New York City, as another example, often ended up in Divisions such as the 77th. This was the pattern for any non-black minority in the United States at the time.

This regional grouping is also useful for examining the issue of “Code Talkers”. While the Navajo Code Talkers are famous for their exploits during the Second World War, the practice originated during the First World War. The first known instance is of Ho-Chunk men (in the 1st Division), while the most prolific use of the practice during the war was by the Choctaw of the 36th Division during the Meuse-Argonne. Other Native groups, such as the Eastern Band Cherokee (in the 30th Division) and Comanche (in the 90th Division) are also known to have been used as “Code Talkers”. This practice of coding messages in languages that the Germans would have no idea how to translate and then to crack the code was only possible because men from those tribes were grouped together on a regional basis and thus enough speakers of their language were available to be used in writing, transmitting, and translating/decoding the messages.

While, ultimately, there was a generalized regional bias to the draft, non-white replacements were not sought to fill any casualties – instead – anyone who was available could be sent to these units. You could be from Texas and end up in the 77th Division, or from Massachusetts and end up in the 40th Division. You could be a Native American from any of those regions and end up in a completely different unit, and so on.

One issue that the AEF faced in this integrated military, containing many ethnic groups and races, was the language barrier. Many of the immigrants who joined the AEF did not know English. In September 1918, as one example, there were over 35 ethnic groups represented at Camp Dodge in Iowa, with over 544 men from those ethnicities who did not speak English. In order to train and fight effectively, the AEF sought to train these men in English so they could at the very least understand orders and have basic conversations.

Initial efforts went poorly, as classes were created on an ad hoc basis and scheduled around regular training. However, in early 1918 the AEF adopted the “Camp Gordon Plan” where all non-English speaking recruits were first assigned to a “development battalion”, delineated into ethnic companies, with Officers and NCOs who spoke the same languages as the men they were training. They then spent hours each day working on English before conducting the rest of their training. This scheme was much more successful, and it also aided morale as these men did not feel so alone in the training camp.

There was a deeper reason for wanting to break this language barrier, however: "Americanization". Service in the military was seen as a path by white American officials to "Americanize" immigrants and minorities, to drop the "hyphen" in their identity and become just "American". They were looking to assimilate these men into American culture. Many minorities also saw the AEF as a path towards citizenship and acceptance. While this was a hope, in practice it mostly failed. Native Americans who served in the military were allowed to apply for citizenship in 1919, and blanket citizenship was offered to Native Americans in 1924 (the traditional argument is that wartime service played a role in the impetus behind this measure). Citizenship, however, in the words of Thomas A. Britten "did little to noticeably change their lives". Other groups, such as Asian Americans, were promised citizenship with their service - but were denied it at the end of the war. Bhagat Singh Thind, an Indian man who enlisted in 1918 and received an honorable discharge, ended up taking his case to the Supreme Court in 1920 where he was denied citizenship once again (although he obtained Citizenship through New York in 1935 after they allowed any military veteran from the war to become a citizen).

I can speak on the Japanese-American aspect of this. Before Japanese-American units had been created, about a third of volunteers were incarcerated at the various interment camps and intemporary facilities around the country (the other two thirds were from Hawaii, which was not a part of the wartime incarceration, although they were under martial law). For the incarcerated men, the matter of serving a country that had detained them in camps was a matter of high controvery, in addition the the requirement of advowing any ties to Japan (those who anwered "no" to the question of military services and ties to Japan, questions 27 amd 28, became known as 'no-no boys'). The vast majority of soldiers in the units were nisei (second-generation Japanese-Americans), and the vast majority of commanding officers were white. A primary goal of the creation of these units was as a Federal Goverment response to Japanese propoganda at the time (which critized American segregation and racism) whilst also presenting themselves as a beacon of democracy. FDR specifically mentioned that the 422nd was formed to show that "Americanism is not, and never was, a matter of race or ancestry". The formation of these units also allowed for nisei men to be included in the national drafts. That being said, these units were largely deployed in Europe, and their families continued to remain incarcerated. In the case of the 422nd, they became famous for their actions in the European theatre, and are the most decorated unit in US military history. Their unit was depleted twice during the War, and more nisei men were drafted.

For further reading regarding the complex national, global and individual power dynamics at play in both the creation, participation, and celebration of Nisei Units, I reccomend "Race for Empire: Koreans as Japanese and Japanese as Americans During WWII" by Takashi Fujitani.

Additional Source: "Voices Raised in Protest: Defending Citizens of Japanese Ancestory in North America, 1942-49", by Stephanie Danielle Bangarth