If you’re using antiperspirant that boasts that it lasts all day, it works by encasing the aluminium salts that make it antiperspirant in microscopic wax beads that are supposed to break open over the day as you move around. This leaves waxy stains behind that are a pain to wash out as the aluminium salts and wax protect each other from detergent and water.

What works is something acidic that will react with the aluminium salts and ideally the wax, too. I’ve had great success soaking t-shirts in water with some sulfamic acid (also available as coffee machine descaler) for a day or two. Vinegar might work, but it’ll be less effective and so take longer and need more, so will be smelly and more expensive.