Try an enzyme cleaner.....I suspect they are not sweat stains bur from some product you are using.

Like Biz?

I am sure they are sweat. I do art fairs outdoors. I need to look "nice", but I'm out there in 90 degrees F plus. I try to change my top after set up and before tear down, but I still get pretty hot in between. I know when I'm soaked in sweat ;)

Do you smoke? If so, it could be nicotine stain.

I jut found some yellowed white cotton trims in my sewing items recently. I put them in to soak with Oxiclean in hot water and then forgot about them.  They soaked for two or three days and came out nice and clean. Perhaps you might want to give the Oxiclean another chance...or just decide to play with tie dye

krissie, no, I am a non-smoker.

Lyndee Lee, The label on the Oxi-clean stated it doesn't work after 6 hours. That's why I put them in the wash at the end of that time.

They all have a nice print or woven design on them, so tie-dye would not be suitable.

I need to figure this out, as it will be a perennial problem.

Hmmm, I agree that it's probably not your sweat per se, especially if you notice these after only one wear. I would look into other culprits. Soap, shampoo/conditioner, deodorant, hair color, hair spray... think about what products you use and maybe try process of elimination. Even jewelry can cause stains like this.  It may even be laundry products  that didn't rinse out entirely. Your sweat may be contributing but it can't be the culprit.
Having spent much of my life exercising, I can tell you that none of my clothes were stained by sweat, even in marathons. Eventually culprits. Have gotten yellow or stains, but those are from antiperspirant.

I know it's sweat. It corresponds to exactly those places where I .... get sweaty! Mostly my back. I don't wash my show clothes every time - they are 100% cotton - they have to be pressed - I don't have time to do that for every wearing. When I can see anything on them, I move onto another one.

My hair is short - not shampoo or conditioner. No hair color or hair spray. No jewelry running down the middle of my back, either.

2 of them have a box pleat at the middle back - so the part touching my back gets stained, not the part that is 2 layers further out. The part shielded from my skin by my bra does not get stained.

My exercise clothes don't have a white background, so I wouldn't see them get yellow.

Until 2 years ago, I never bought anything with a white background. But it's so hard to find sleeveless woven, not knit, all-cotton tops now, that look halfway nice for selling my work to the public on 100 degree days, that I was forced to buy these.

So now I'm dealing with this problem....

I was trying to say that it's possible your sweat, as it runs down your back, is carrying the chemical that's staining your shirts but it isn't your sweat itself that's the problem. Yellow pit stains occur because of aluminum in antiperspirant and salt, not just sweat. You're not getting these stains in your armpits though, which is why I suggested looking at the products you use. Whatever might be on your skin/ in your hair/ around your neck, or whatever you might use in the laundry could be the culprit.
Enzyme based detergents are recommended for removing antiperspirant stains. You could try that.

Dab the stains with ammonia diluted 50% with water, then rinse with cold water and wash as usual. Hope this helps you

My new go-to for stains is: 2 cups hydrogen peroxide, 1 tbsp baking soda, 1 tsp Dawn in a spray bottle.

Here is the link: https://www.theartofdoingstuff.com/tip-weekgetting-rid-of-cat-pee-smell/#mv-creation-157-jtr

Soak for several hours in Tide With Bleach POWDER and warm water.

Sweat will come out with just warm water (105F or higher). It came out of your body at 98-99F so it will re-liquify at the same water temp of higher. Normal enzyme based detergent will bind to and carry away sweat. Tide (any variety), Persil, etc. would work great.

If these are not working then the stain is not sweat.

"I don't wash my show clothes every time - they are 100% cotton - they have to be pressed - I don't have time to do that for every wearing."

This might be a big part of the problem. The longer body oil, perspiration, and anything else sit on fabrics, the stain "sets" and is harder to get out. A detergent that is mediocre on removing body oils and perspiration that have "set" is not going to be up to the task, either. (some are better than others according to CR magazine) Especially in summer, we wear something once then it goes into the wash.