Unfortunately, the media and governments do a very poor job of outlining the whys of radiation, and leave it a very scary boogeyman for concerned citizens.

Iodine pills don't magically protect people from radiation. Taking them doesn't do anything to prevent nuclear decay from happening, doesn't grant people superpowers to stand in a radioactive environment, and doesn't let you lick fuel rods without consequence. In fact, taking them is to leverage the chemical benefits of diffusion.

Before I dive right into it, let me mention that a few forms of radioactive decay don't impact humans well. Alpha decays bounce off your clothing and skin, and can only travel a few cm in air. Beta decays bounce off your skin, or only make it so far into the already-dead skin cells, and don't travel very far in air either [0]. Gammas (sunlight) are a different matter, as are neutrons (from nuclear reactors). Hence, the sunscreen and the giant concrete containment units. This all changes if you inhale/ingest radioactive isotopes, and alphas suddenly become the most deadly (ask Alexander Litvinenko) and betas are up there too. Iodine 129 is a beta emitter, a pile of which will continue emitting radiation long after this generation of human beings are ash and dust. Eating this stuff is like eating glass.

Back to the iodine pills: You take this pill because $GOV says so, and it saturates your body (thyroid) with a stable isotope of iodine. It's like taking a half-empty biological sandbox, and filling the rest of it up with sand. The inner child that lives within us can continue playing safely as this iodine doesn't decay. It means no new iodine 129 will be able to be retained in your body, your body is already full of the stable stuff, so such a person will still ingest iodine 129, but won't retain it in their body for a long period of time.

However, failing to take an iodine pill beforehand will mean the sandbox is half-empty when a nuclear fission accident releases iodine 129. This means that sandbox will become (over time) quarter-sand and quarter-glass and still half empty, due to the laws of diffusion. No inner child wants to play in that box. And that means iodine 129 is sticking around inside the body, and in particular the thyroid (which is an organ more sensitive to radiation than others, for reasons I don't know since I'm an engineer not a doctor).

So, how does this stack up against ruthenium?

Your body doesn't use ruthenium in any significant way. It'll just pass it right back out. You can think of it as your body being permanently on the ruthenium pill. Yes, ruthenium 106 is a beta emitter exactly like iodine 129, but with a much shorter half-life of around a year. It decays to Rhodium 106, another beta emitter, which within a minute is already burned out into stable palladium 106. So on the whole, the human body is going to have an extremely tough time concentrating this stuff to dangerous levels inside of it.

So overall, your risk is not zero, but if you want to offset it I recommend not taking an airplane the next time you otherwise would, as flying up at cruising altitude in the atmosphere usually exposes you to more radiation than ruthenium 106 scattered around the earth ever will.

I highly recommend playing with [1] for nuclide information and decay chains.

[0] https://www.youtube.com/watch?v=Efgy1bV2aQo

[1] https://www-nds.iaea.org/relnsd/vcharthtml/VChartHTML.html