Not a stupid question at all. And unfortunately, I've seen it happen.
The short answer is...don't start the engine if you catch it in time.
Brake fluid and transmission fluid may both be called "fluids," but they're designed for completely different jobs.
Brake fluid is made to work in a sealed hydraulic braking system. Transmission fluid is designed to lubricate, cool, operate hydraulic circuits, and provide the correct friction characteristics for clutches and bands.
The biggest problem is that brake fluid attacks many of the rubber seals used inside an automatic transmission.
It can cause seals to swell, soften, and eventually fail.
Now, if someone accidentally poured a few ounces into the transmission and realized it before starting the engine, you may get away with draining it and servicing the transmission immediately.
But if the engine is started and that brake fluid gets circulated throughout the transmission, the risk goes up significantly because it reaches every valve, clutch, servo, and seal.
One thing I've learned over the years is this:
Not all fluids are interchangeable just because they're liquids.
I've seen people accidentally add engine oil, power steering fluid, coolant, DEF, and brake fluid to the wrong system. Sometimes the mistake is recoverable. Sometimes it becomes a very expensive lesson.
The key is this: The sooner you catch it, the better your chances of minimizing the damage. If it happens, don't keep driving it hoping it'll "work itself out." Stop, figure out exactly what was added, and deal with it before it circulates through the entire system.