Echoing what John Leader wrote, basically, you're riding around in a plastic egg-shell, with little true protection from side impacts. Only one of the cars on this site has, to my knowlege, a side impact beam in the doors, but that may be, in my opinion, of minimal benefit in a sub-compact crash, and little or no benefit against a full-size SUV or truck (since the SUV bumper is probably higher than the door beam).
None of these cars have air bags.
While some have "roll bars", many are for decorative purposes only, and would offer no protection in a real roll-over. Some have stronger roll bars, but only a few cars have bars that would be beneficial in a roll.
Most have been fitted with a portable fire extinguisher by their owners (thankfully, they almost never get used!)
Probably half of the Speedster replicas have improved ignition systems (point-less ignition), although only a handful have modern fuel injection. Some are fitted with catalytic converters and may pass local DMV emmissions testing, but the majority are exempt, due to their age.
Some have the original "collapsible steering column" which was fitted to their donor cars starting sometime in the mid-sixties. Still, not a lot of protection, and upwards to 40 year old technology (if it was used at all).
All of the current manufacturers provide seat belts and will customize belts per customer requests. Some have 2 or 3 point seat belts installed by their owners which may or may not provide adequate protection, depending on how (and where) the belt anchors were mounted.
None of them have ABS braking, although many have newer-technology disk brakes fitted, at least to the front wheels. None of them have computer-controlled accessories (except for basic ignition control), so little goes wrong of an electronics nature.
Most have much safer (radial) tires than were fitted to the original Speedsters of their day, often somewhat larger than original , too, affording much better handling. Handling is often improved on many of the replica's by the addition of anti-sway bars, and the Speedster versions sit lower to the ground, giving a lower center of gravity for better handling, too.
All of them have the minimum safety features required by the DMV in their respective states (at least when they take them for inspection).
Having said all that, only a handful of these cars are driven every day - most are used on weekends and the occasional week day for errands and just cruising windy back roads (where the SUV's usually are few) for the pure enjoyment of it. It is still felt that driving a Speedster replica is inherently safer than riding a motorcycle (and often slower, too) and can provide a level of nostalgia, fun and excitement that can be found in no other auto of this day.
THAT's why we drive them!!
Gordon
One of the "Speedstah Guys" from Rhode Island