Safety is the top metric for roller coasters, and the main thing they are built to be (other than fun). Because of this, safety can largely influence what style a coaster is, as well as the operations behind it. An example of this is block zones. Having lots of block zones means lots of trains, however the more trains on a track, the more likely a cascade is. A cascade is when trains are forced to stop throughout the ride at the end of the block zones, due to a stoppage further up. This can be something like a handicapped rider, or a problem with a restraint. A cascade, while safe, causes unnecessary panic for riders, and significantly diminishes the ride experience. Because of this, many coasters will experiment to determine their optimal range. Even though Hagrid's Motorbike Adventure could theoretically have 12 trains on the track, they usually only run 10 at a time, as 11 and 12 the timing for the trains launching is very precise, with much more frequent cascading.
Another safety measure is the console design for operations. Consoles are designed to make the action that needs to be taken more intuitively. This means that similar rides will have similar consoles, so that an operator can know the general area they need to look for a control right off the bat. There are also safety features like the E-stop, or emergency stop. However it is important to keep in mind that E-stops are not always the right course of action (~50% of the time). Most times when there is an issue on the coaster, an E-stop should be a last resort, as it is a very abrasive stop on the riders, and can cause other operation problems. Newer monitoring and computer systems are helping in this regard as well. Having more concrete block zones, and better braking sensors and protocol has prevented many scenarios in which an E-stop would otherwise need to be used.
Below are several different control panels for different coaster types. Notice how they all have some form of button or color coding to differentiate functions.
Another form of safety is the restraints used on rides. There are a myriad of restraints, from lap bars to over the shoulder harnesses, and each is designed based on the acceleration and thrills associated with the ride. By customizing restraints, it allows rides to fulfill a much wider range than if there was a law that all rides must include lap bar restraints. This is another way coasters will balance safety with fun. Sometimes a coaster will be developed just on the edge of what is acceptable for a certain type of restraint, or use a more unique restraint to add to the thrill factor. Take Cannibal in Lagoon. This coaster uses a lap restraint, unlike many other coasters with its ride scope which use shoulder restraints. This adds to the thrill for many passengers, as they feel the restraint is "new" and therefore not as trustworthy, despite being just as safe.
Along with this, as previously mentioned many rides will have a computer monitoring restraints, and will not launch until all restraints have been fastened, which may slow down the loading process but will increase safety measures.
More basic things to keep in mind with safety is the coaster design. Coasters are designed to safely excite people, and as such, have limits put upon the ride. There's a reason not every coaster has a double loop, and its because the calculations between thrill and safety are important. This includes things like calculating the max speed, gravity on tracks, and how many seats should be on each train! An example of this is in Universal Studios. Their newest thrill coasters have a lower train capacity than older thrill rides in the area (24 seats). This is because Universal has done research into the thrills they aim to provide, and determined that even though throughput will be lower on these rides, the ride itself is able to offer more thrills in a safer manner.
This is also why coasters will diversify ride portfolios. Having rides that appeal to large masses of people with fast hourly capacity can help balance more extreme coasters and keep them from having issues with overloading.
Having a focus on safety allows roller coasters to be designed to be fun, with low incident rates.