On the way to an emergency? Of course they should. And people should pull over.
And only sometimes while on the job. For example, if they catch someone for speeding and happen to go through a red light, I don't find that to be a grave thing. Speeding is easily a public hazard. Going off to investigate a theft where the thief has left the property, though? No need to run the light as the delay won't make a difference. Going to a car accident, especially with hurt folks or that is blocking traffic? Yes. Car accident in an open section of parking lot? Rarely necessary.
Ambulances, sure. Firefighters? Yeah, usually. Cops? You'll have to convince me if you are talking about midwestern American cops. I know they go through lights... because. Or they'll hurry to something non-vital, where there is no one getting hurt, yet scurry none-the-less. I never realized how common this sort of thing was - lights and freaking sound - until I moved away.
Are you listening to the police scanner or something? How do you know where or how they have been dispatched?
I live in a small northeast city off of an avenue where there are two trauma centers, a firehouse that does about 5,000 calls/year and a police HQ. I see and hear plenty of these vehicles. When you see it enough, you can spot the different patterns in how police, ambulances and fire trucks respond.
1. I know the cops do the light thing simply by knowing a few cops.
2. I don't know where they are dispactched or anything. I could tell the difference between sirens though.
3. I know not all dispatches are emergencies that need lights, sounds, or running lights. If someone has broken into your business, for example, and the person is no longer there, there is no need for speed, lights, and so on. I'm in a larger city in another country now... and there are less sirens and stuff here. It is really weird. I know they respond and the crime rate is probably lower, but... priorities are different as well. I generally didn't see the same patterns with fire trucks and ambulances in the states, and honestly never had a complaint about them. Just the police.
Those protocols are why something like 95% of the time when you see an ambulance with the lights on there is nobody in the back. (The worst case of a broken leg is serious internal bleeding that only an expert can detect, then they get there and it is just a broken leg)
On the way to an emergency? Of course they should. And people should pull over.
And only sometimes while on the job. For example, if they catch someone for speeding and happen to go through a red light, I don't find that to be a grave thing. Speeding is easily a public hazard. Going off to investigate a theft where the thief has left the property, though? No need to run the light as the delay won't make a difference. Going to a car accident, especially with hurt folks or that is blocking traffic? Yes. Car accident in an open section of parking lot? Rarely necessary.