The idea that a 20 year old car is unsafe is auto industry FUD. Yes, there have been great safety advances since the 1970s and 1980s. They've kind of tapered off though. I would absolutely trust my family's lives in any year 2000+ vehicle.
Airbag and crumple zone safety requirements for crashes that aren't head-on are much more recent than the 2000s. Many car makers designed their cars to pass those, but will leave you dead or worse if you get T-boned.
ABS wasn't even a requirement in the EU until 2004, and American cars could be sold without ABS all the way until 2012, when traction control was also made mandatory (which the EU then also followed).
Things like the slightly-angled side pole crash test was only added to the Euro NCAP in 2015 and was updated five years later to make it a bit more realistic, though cars still woefully fail in many real-life scenarios.
I wouldn't really consider a car "safe" unless it passes the ~2015 requirements for car safety well. A well-designed car full of optional safety features from the ~2010s is probably also safe, but I wouldn't count on it unless you've done research into it.
I believe Volvo has had a reputation of being ahead of the curve with these kinds of crash safety tests, but even they had to improve over time.
> I would absolutely trust my family's lives in any year 2000+ vehicle.
I work partly in prehospital emergency medicine and I wouldn't.
I already feel uneasy with our 2017 EuroNCAP 5 star SUV due to the improvements since then, in particular AEB and increased structural crash-protection, which greatly change the injury profiles of accidents.