This is a question I've been pondering for several years now. My conclusion, based on the way people behave is NO, they generally do not care about safety -- its something they assume (incorrectly) that someone else will take care of for them.
ex. Houses. Someone buys an older house and they just assume the electrical system in it is "safe" if everything "seems to work".
Nothing could be further than the truth. I've done a lot of electrical work on older places, and even a relatively new place that's only 20 years old does not meet the same electrical code standards a new house would have to. Now some of those code changes in the past 20 years aren't "safety" related, rather they are convenience or usability related and that's fine. The place may be a PITA from a usability POV, but usability issues usually won't kill you, they're an irritant.
Some of the changes however were safety related. There are more locations calling for GFCI(ground fault circuit interruptor) protection now than 20 years ago. The last 5 years have seen the advent of the ACFI (Arc-fault circuit interruptor).
Does it make sense to spend $30,000 on a new SUV only to park it in a garage of a place that might burn down around it, or kill you before you even make it to the garage in the morning? Why do people resist spending a couple of grand to make a house electrically safer for themselves and their children yet they have all sorts of money for new cars, fancy kitchen/bathroom upgrades, tile floors, etc?
Seriously, what's up with this mentality? Lack of a fancy faucet never killed anyone - but lack of a $12 GFCI where one was called for kills people every year.
UPDATE: If you have a panel with breakers that look like the pic below, consider getting rid of it. It is a FPE panel and they are PURE EVIL and prone to starting fires.