Rail travel is inherently extremely safe and the UK has one of the safest railways in the world. There is an ugly issue at the moment with trackside worker fatalities that feels like it isn't getting enough attention but for passengers and train crew the chances of being killed or even seriously injured whilst travelling/operating a train are remote. Thanks to the efforts of many people over many years developing systems of working, technological solutions, and designing equipment that is robust both inside and out the railway is extraordinarily safe. Therefore travelling on an HST for both driver and passenger is extremely safe. I have no doubt that the driver has a higher risk of death or serious injury making their way to or from their signing on point each day whether that be on foot, by cycle, or car than they do whilst they're in the cab.
That being said the HST itself, in the context of the fleet of vehicles in service today, is on the poorer end of crashworthiness. It is probably not the poorest in service but in comparison to stuff which has the advantage of several decades of advancement in design it is poorer. Certainly from the point of view of the driver. One only need to look the metalwork that surrounds a modern cab to see that the safety and survival space of the the driver is now actually a consideration.
Given the severity of the accident at Stonehaven the likelihood is that there isn't a vehicle in service in which the driver would have survived. Whilst something like an LNER Azuma would have probably physically held together rather than disintegrating like the HST cab did the impact forces that the driver would have gone through almost certainly would have been fatal (though I'm not a doctor!). It might have been better for passengers in the consist as a modern vehicle is less likely to have been as crushable as the Mk3s in the formation were but again the likelihood is that even a modern vehicle would have seen passenger fatalities.
HSTs are pushing over 40 years old, they have been worked hard over that time and have given excellent service. In many respects the passenger environment they provide is better than that provided by modern replacements (which is due to the people specifying trains, rather than something that need be inherent to new stock) but they remain increasingly geriatric.
Therefore it is logical that HSTs should be replaced and replaced soon. They are old. They are due for replacement. That they are not as safe as other stock on the railway is neither here nor there. It is true that they are not as safe as modern trains, but considering the inherent safety of operation on the railway it is not something that means that they need to be immediately withdrawn.
Making plans to withdraw them from service is logical and wise. The industry as a whole would benefit from some sort of wider rolling stock strategy (that old "single guiding mind" thing again!). But there is no reason to blackball them immediately.
So are HSTs considered unsafe? I wouldn't have said so. They are not as safe as modern rolling stock but thankfully the inherent safety of rail travel means you are already starting from an extremely high level of safety.