I think bremsstrahlung can be a problem. When the easily stoppable alpha or beta particle hits something heavy, conservation of energy requires it to convert its energy, often to something far more dangerous - a gamma particle/ray. Those are not easily stoppable, and can do some serious damage. If you have bad luck.
I've read that keeping the active object behind acrylic or aluminium can allow the particles to slow down, and reduce this type of radiation.
Would be interesting to hear if there are any physicists on the forum that knows something about bremsstrahlung.
I am a physicist, but I am not a health physicist, which is why I keep referring people to the Oak Ridge Museum of Radioactivity page at
https://www.orau.org/health-physics.../products-containing-thorium/camera-lens.html , because that page is written by a health physicist with a strong historical interest in these issues. Other websites of interest include
https://www.epa.gov/radiation/radionuclide-basics-thorium and
https://www.epa.gov/radiation/calculate-your-radiation-dose and the NRC's NUREG-1717 report section 3.19 on the exemption for "Thorium in finished optical lenses":
https://www.nrc.gov/reading-rm/doc-collections/nuregs/staff/sr1717/index.html
To give a baseline comparison, the Oak Ridge page reports a calculation (from the NRC's NUREG-1717) that a "serious" photographer carrying a camera with a lens containing thorium for 30 days x 6 hours/day, might receive an annual exposure of 2 millirem. (The more extreme example would be a person using a thoriated glass eyepiece for long periods at work, such as a TV cameraman, but thoriated glasses in eyepieces seem to be rare and I doubt there are many TV cameras left from the time when thoriated glass was in use). This includes all the products of the decay chain, betas, gammas and so on. For comparison an ordinary person's annual exposure is of order 100-200 millirem - see the EPA calculator linked above. 2 mrem is the exposure from flying 2000 miles on an airplane.
This is why I keep saying that these lenses ought to be safe but don't store them under or next to your bed. The proximity and duration of exposure matter.
The danger of radiation depends on activity, energy, and proximity. The worst thing is if you swallow or breathe the radioactive element (why eg radon gas is bad). Fortunately in camera lenses the thorium is solidly encased in glass. Thorium mantles for camping lanterns could lead to more exposure, although even there I think the real problem is for the workers who made the mantles.
Thorium has an extremely long half life which is why it is still around. That means its activity is relatively low (decays per second) so even though it emits some betas and gammas, the rate of exposure is small.
Bremsstrahlung ("braking radiation") is the production of X-rays when energetic electrons (betas) are scattered, in this case off atomic nuclei. Heavier elements produce more intense bremsstrahlung, I believe because the heavier nucleus has less recoil and the electron is decelerated more quickly. The wiki page on bremsstrahlung gives the example of phosphorus-32 and the (counter-intuitive) need to shield it with a thick layer of light material rather than a thinner layer of lead. But there are a couple of reasons why this isn't a general concern. First, phosphorus-32 is extremely active: it has a half-life of 14 days (vs thorium-232 at 14 billion years) - the activity of 32P is ~300 tera-Becquerel per millimol (a few tens of milligrams) vs camera lenses measured at ~10 kilo-Becquerel (from NUREG-1717). Second, both betas and X-rays are absorbed/scattered by a reasonable thickness of ordinary materials, perhaps a meter of air for beta rays, solid material for X-rays. Despite Superman, you can't really see through a wall with X-rays. Anyway, I'm pretty sure this effect is minor for thorium and that it is taken into account by actual health physics analyses.
Anyone with a strong interest/concern in the subject should read NUREG-1717 section 3.19 carefully:
https://www.nrc.gov/reading-rm/doc-collections/nuregs/staff/sr1717/index.html