It's not unsafe in the sense that they will immediately have a reaction and be harmed by it. (I've actually read a lot of the research on this).
What the advice is about is an increased risk to young babies from spending longer time periods in car seats. Ideally, very young babies ought to be laid flat as much as possible. The risk with an inclined position such as a car seat (but also things like bouncers, rockers, swings, and pushchairs in semi-reclined position) is that they can end up in a position where their airway is compressed due to poor neck control at this age. If you bend your head down, so your own chin touches your chest, you can feel how difficult it is to breathe like this. The problem for newborns in particular, is that they can't hold their own head up to alleviate this, particularly against the slope of the seat. And while they might be able to manage a reduced level of oxygen for a short amount of time, the longer they are left like that the less oxygen they are taking in, so in rare cases, it can cause seizures or even asphyxiation (suffocation).
Really the riskier duration is 1hr+, especially if your car seat is modern (car seat inserts have greatly improved since a lot of these research observations were made) and properly adjusted, and your baby is full term and a typical weight with no breathing problems. But even this is a small increase of a small risk to begin with. Certainly when my 16yo was born, everyone was using swings and rockers and bouncers for tiny babies and nobody ever told us not to. You could even get a hammock bed for them to sleep in which would cause all kinds of worry today! I am sure I don't remember car seat time limits being suggested either, although there was a lot of criticism of people using car seats on pushchairs and suggestion that it would curve the baby's spine due to the lack of proper support, and I remember being warned never to put the car seat on a high up surface in case the baby managed to rock themselves off the edge of the table (which has also been a cause of accidental death to babies in car seats).
The 30 min advice seems to come from a small pilot study done in 2014 and it is strange how the UK has really latched onto this, because IMO there were a lot of problems with the study design and none of the findings have been replicated since. However I am curious about @GoneIsAnotherSummersDay 's comment - it makes sense, because babies in rear facing car seats hardly ever die in car crashes, but I hadn't come across this statistic before and I'm curious if you have more info. I would imagine that it can't be that many, because the figures from the US over various multiple-year spans are in single figures per year, and they drive much more and have much higher population than the UK.
In any case, for babies over 4 weeks old, the recommended guideline is 2 hours. Under 4 weeks, you just want to minimise use of the car seat where possible, or keep a guideline of 30-60 minutes in mind. If you choose to use the car seat on the pram or go for a long drive, it is enough to remove them from the seat, give them a cuddle (maybe a feed) and let them stretch and then put them back in the seat if you need to continue your journey.
And these are just guidelines too. You can make your own judgement on whether or not something is safe. IMO the way that people interpret guidelines today on the internet is extreme and not the intent of the advice. It is anxiety fodder, when in reality you really don't need to do everything 100% right all the time. Your baby will probably be fine even if you did everything wrong! After all, the majority of babies were fine even before this advice. While it's useful to bear it in mind and be aware that a particular risk exists, and the ways to reduce the risk, I don't think it is healthy to be worrying constantly about tiny risks which likely will not happen.