I own a T6i and a 6D. I'm interested in tethered shooting for studio scenarios. However I've heard from a friend that if I tether my camera to my laptop and I a power surge happens in the USB port, that it can fry some board on the camera and I'll lose it. Can this actually happen, and if so, is there a safe way to perform tethered shooting?
I wouldn't worry about it. From my experience, power surges are not something you need to worry about with USB devices. If a power surge happens, it will most likely be from the power grid which is more likely to fry the computer you are tethering from, than the USB devices connected.
Usually the opposite happens. A USB device draws more power than the USB port allows, which is what is generally meant, when discussing USB power surges. But that won't break anything, only potentially cause some of the other devices connected to not function properly until being hot-swapped.
Tethered shooting should not be a problem.
As another answer correctly states, power surges on computer USB ports are not very likely. Also, for such a surge to be harmful, it would need to be an actual overvoltage between pins on the USB port. Unlikely unless something manages to activate eg USB PD modes by accident.
There is slightly more likelyhood of the whole usb port having problematic potential differences with OTHER power supplies involved, or relative to ground.
For absolute maximum safety of expensive equipment, avoid connecting the camera to USB PD (Power Delivery) capable ports, avoid using less than trustworthy powered USB hubs, and avoid having anything else connected to the camera that is also indirectly, in any way, connected to the mains (eg studio strobes, HDMI monitors...). If there are multiple cables plugged into the camera, only one cable should be connected to anything that is plugged into the wall or connects to something plugged into the wall.