One of the missions for naval progression wants me to bring combat stabilizers to them, except combat stabilizers are illegal in pretty much all jurisdictions. What happens if I get caught bringing them back? Do I get a bounty on the spot? Does the station initiate lethal response?
Answer: You never get shot on sight for smuggling, instead it is an instant fine.
Additional info: The fines are usually a lot higher than the value of the goods that you are smuggling, meaning that you really don't want to get caught.
If you don't pay the fine within a certain time (which was 24 hours last time I checked), it gets converted into a Bounty and, if I remember correctly, you become wanted by the faction that issued the fine.
The easiest way to avoid being fined is to smuggle into an Outpost, at which there are usually - but not always - no patrolling security ships (it is the security ships that scan you, not the station), however be warned: Outposts that do have security ships are harder to smuggle to than normal stations because you are always visible. With a normal station you can usually break the scan by flying through the station entrance.
Obviously, if you are smuggling for a mission, you don't have the luxury of choosing where you smuggle to, you have to return to the station that issued the mission. There is a lot of advice on the internet about how best to avoid being scanned. Personally I keep about 8KM away from the station entrance, lined up ready to dock already having requested permission. I disable everything except my thrusters, scanner and power distributer. I boost to get to full speed then cruise towards the station at max speed. When getting close, I hit Silent Running, turning it off as soon as I get into the entrance as well as hitting reverse and dropping the landing gear to slow down.
I've never got a fine with my method, although a couple of times I have had a scan start as I'm nearing the entrance. It doesn't work well for all ships - some don't slow down fast enough as you go through the entrance and some overheat too quickly for the silent running. You just have to find a system that works well enough for you.