It's relatively fine to continue your journey when the amber or red ABS light turns on while driving, but you'll need to be cautious while doing so. The ABS light means the antilock brakes may not function correctly, but it doesn't mean you don't have brakes and can't stop the vehicle.
The ABS (or antilock braking system) does exactly what it sounds like, preventing the wheels from locking up when pressing hard on the brakes. In older cars with no ABS, pumping on the brake pedal is necessary to prevent wheel lock and loss of steering control. The ABS does this using wheel speed sensors and an electronic control module to pulse the brakes around 15 times per second or more. ABS also allows safer, controllable panic stopping with a single pedal push.
Since the ABS is not working, you should reduce your driving speed and increase your distance from the car in front of you, especially when it's raining or you're driving in snow or ice. And take the car for servicing ASAP. Factors such as insufficient brake fluid, wiring faults, a bad wheel speed sensor, worn brake pads (unlikely to be the case with a Tesla), or blown fuses can trigger the ABS warning light. Loose wheel hubs or damaged wheel bearings can also cause the ABS light to turn on, since those parts could affect sensor readings.
Most cars have two brake-related warning lights on the dashboard. The red or amber ABS light warns the driver of potential issues with the antilock braking system. There's also a red brake warning light that could turn on if it detects low fluid levels, worn brake pads, an engaged parking brake, or faulty wiring.
If the brake warning light illuminates after starting the engine, don't continue driving, Have the issue checked immediately. If it turns on while driving, don't panic: You can still stop the car, although it may require more braking effort. However, it's better to pull over, stop driving, and call for assistance if both the ABS light and brake warning light are on, since it could mean a massive fault with the entire braking system.
The mechanic will most likely inspect the entire braking system and check if the pads and shoes are worn, replenish the brake fluid, check the condition of the brake rotors, and test the ABS sensors, among other things. For reference, periodic brake servicing is necessary at least every 5,000 to 7,000 miles (or twice a year), and the brake pads will most likely need replacing every 30,000 to 35,000 miles.