I just was given an excellent link that helped explain how my mother had been involved in a Texas high school group wearing swastikas on their uniforms. I've updated this post to remove the German American Bund quote, and added fellow blogge, Mike Brubaker's information instead. Thanks Mike! His earlier comment is at the bottom of the post.
I've done more research, Barb, and I think I have found the answer to your mystery. As I discovered last week, in the 1930s there were a large number of "Swastika Clubs" in America and surprisingly there were many in Texas and in San Antonio too. Some were connected to a women's organization called Royal Neighbors of America that was associated with the Woodmen of the World fraternal order and still exists as a life insurance company. This group sponsored "Swastika Clubs" to encourage young women to enter the business world. They also liked to play bridge. But I could not find a direct connection to any San Antonio high school.
There was also a "Swastika Club" in San Antonio's Mexican-American community in the 1930s that was also for young women. It sponsored society balls and other benefit entertainments but its membership seemed to be just Hispanic people and it was not affiliated with any high school.
Then I found a couple of 1930s yearbooks from Jefferson High online that let me check if the swastika was possibly a school symbol. Obviously Thomas Jefferson High School had better history to use for symbols, mascots, and school names, but the yearbook had numerous photos of members of the school's ROTC and the swastika should patches were very clear on both boys and girls.
With a little more digging I found the answer. The swastika was once an insignia of the 45th Infantry Division, an infantry division of the U. S. Army, mostly associated with the Oklahoma Army National Guard, from 1920 to 1968. You can read about their history in Wikipedia which has a picture of the same swastika patch. https://en.wikipedia.org/wiki/45th_Infantry_Division_(United_States)#Inter-war_years
The patch design was borrowed from Southwestern Native American symbols and approved in 1924. Though the 45th Division was a National Guard unit based in Oklahoma it recruited from young men throughout the southwestern region. As school ROTCs were being developed they used the uniform patterns of the nearest military units, so that's how the swastika patch became part of Jefferson high's unit. As the Nazi party in Germany came to power in 1932, the army sensibly decided to change the shoulder patch and in 1939 chose a Thunderbird symbol created by a Kiowa artist to replace it. Like many traditions it probably took time for schools to change too. Here's another website with some of the history:
https://www.thehistoricalfictioncompany.com/post/the-american-ww2-soldiers-who-wore-swastikas
The American use of the swastika in the 1930s was not associated with the rise of Hitler and the German Nazi party. A search through the newspaper archives found lots of "Swastika Clubs" but absolutely none included any reference to fascism, German nationalism, or Hitler. It was a design that unfortunately became connected to hatred and violence and forced many innocent organizations and even the the U. S. Army to abandon it. Though there were small groups of American fascists that formed in the 1930s, I fell confident that none of them were connected to a high school in San Antonio.
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Here're my photos from my post which shows 1933-34 Texas high school extra-curricular activities from their yearbooks. One photo with cut edges was in my mother's photo album..
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Edited from - Thursday, October 23, 2014
More uniforms
I continue sharing old yearbook pictures of my parents when they were in high school
By 1933 my father had met my mother probably, in Jefferson High School in San Antonio, TX. She signed her name (Mataley Munhall) by her picture below, the right column at the bottom of portraits. Is she in Company C's group picture? Yes, front and center (well, to the right of the tall young man in the very center.)
I don't think my father (George Rogers) was in Company C until 1934. Then he was listed among the members, but I can't find him in the crowd (photo below). But where is my mother in 1934?
Mataley went to the newly formed Company D in 1934...and she was then listed as a sponsor. I think George missed his chance, (that time) since she changed her marching company. Incidentally, like many yearbooks, the group picture below does not have my mother located in the place that is indicated by her name. She is actually the girl in the middle of the front row, with her eyes closed. I know you were wondering about that!
I mentioned before how these young people wore a swastika on their hats...
(HERE).
When I remember Hitler's youth troops, it is even possible that his influence came into south Texas through the German connection. These high school students certainly appeared to have enjoyed wearing uniforms. Here's another post about
The Girls who liked to March. And another one with similar photos
HERE.Yes the club was made of young women who met "as a social aid to the Battalion"...and were called the Swastika Club. I'm sure the young women stopped using that insignia in the early 40s.

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I have often wondered how her grandfather being German American would have influenced her. And of course many other German immigrants lived in the San Antonio area.
Sharing again with
Sepia Saturday!
PS: The first comment by Mike Brubaker with more information than I had before:
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I posted his later comment to this blog at the top, since it summarizes the use of the swastika symbol for the Thomas Jefferson High School.