In both wars, German-Americans were seen as a security threat. Woodrow Wilson said he did not believe they could assimilate into America. They got the nickname "Huns" during WWI. During WWII, they were not controlled as tightly as the Japanese, but German Americans were suspected as having disloyal elements in their communities interested in helping Germany during the war. "By February 16, 1942, the Justice Department had interned 2,192 Japanese; 1,393 Germans and,264 Italians."
You can read an account of this in the section "Germans and German Americans" from:
Personal Justice Denied: Report of the Commission on Wartime Relocation and Internment of Civilians
Link from the National Archives: https://www.archives.gov/files/research/japanese-americans/justice-denied/chapter-12.pdf
This resource does not cover popular prejudice against German Americans but it does give a detailed outline of what the most responsible people during WWII were thinking and doing. This can be part of a baseline for evaluating your question.
I can speak to what occurred in Texas specifically during World War I.
During World War I in Texas, which had nearly 45,000 German-born Texans and over 140,000 Texans of German heritage, there was significant prejudice that led to violence and more.
German-language newspapers came under assault. German-language instruction in parochial schools moved local defense councils to suggest their closure (although it wasn’t done due to constitutional reasons). Church services (Lutheran) conducted in German came under assault.
In areas with heavy German settlement like Fayette, Austin, Comal and other counties, there were attempted lynchings, and a number of floggings.
A few Germans committed suicide. One killed himself when he feared crop failure wouldn’t allow him to purchase pledges war bonds.
There was no evidence, however, of disloyalty among these Texans. Even the German-language newspapers (of which Texas had several) promoted American patriotism.
Source: Sonntag, Mark. “Fighting Everything German in Texas, 1917-1919,” The Historian, Summer 1994, Vol. 56, No. 4.