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In Rhodes' The Making of the Atomic Bomb, he says that, while Pu is not that radioactive (which is surprising -- maybe he means compared with radium and some other elements), it is very toxic.
I would guess it could not be much more toxic than uranium (U) or lead (Pb) -- I believe thallium is more toxic than U and Pb and so is mercury (Hg). If it is more toxic than lead, do we understand the mechanism?
The toxicity is primarily due to radioactivity and to absorption by the body, where that radioactivity can act internally. There is, "significant deposition of plutonium in the liver and in the "actively metabolizing" portion of bone," according to Miner and Schonfeld.
Many $\ce{Pu}$ isotopes are primarily alpha-emitters, with "high energy radiation with low penetration and thereby requires minimal shielding. A sheet of paper can be used to shield against the alpha particles emitted by plutonium-238," from Wikipedia. The risk of holding a small amount of plutonium, if it is sealed inside almost any container, is negligible, because the the heavy, positively-charged alpha particles are stopped by the container in a very short distance.
By that same token, when absorbed, the plutonium migrates to rapidly dividing liver tissue and bone's hematopoietic cells. The alpha particles are stopped in a very short distance, depositing all their energy in the few nearest cells and massively interfering with cellular reproduction. Small amounts can cause various types of cancer, such as leukemia, a cancer of the previously-mentioned blood cell producing tissues.
That said, plutonium is not quite as toxic as one might think: "The U.S. Department of Energy estimates that the lifetime cancer risk from inhaling 5,000 plutonium particles, each about 3 µm wide, to be 1% over the background U.S. average... no human being is known to have died because of inhaling or ingesting plutonium, and many people have measurable amounts of plutonium in their bodies."
Perhaps what Rhodes means by "not that radioactive" is that the radiation from plutonium is not very penetrating. The isotope used in nuclear weapons, 239Pu, has a half-life of about 24,000 years, comparable to radium, or to 231Pa. If I've done my math correctly, one mole of 239Pu, about 6e23 atoms, with half-life of 8e11 seconds, should emit about 400,000,000,000 alpha particles per second. Of course, if it were a sphere, most of those particles would be absorbed inside the mass of metal, releasing energy as heat. However, spread through a human body, each particle has a much greater chance to cause damage. And 238Pu, used in radioisotope thermoelectric generators, is far more radioactive!
Actual toxicity other than radioactivity is not, as far as I know, very well studied. Quite simply, most of the danger is the radioactivity in general, as well as the toxicity of decay products (uranium and americium).
Basic knowledge of biochemistry though suggests that it should be toxic for the same reasons that most high atomic weight metals are, namely that most biochemical processes do not differentiate well between elements beyond the ionization charge (this is why rubidium and cesium salts are toxic, the large ion size for both of them combined with the +1 ionization state causes them to get stuck in and block potassium and sodium ion transfer channels in cells). The tendency of plutonium to concentrate in the liver and areas of bone growth supports this, as both are areas where ions with similar charges tend to concentrate (note that plutonium ions can be anywhere from +2 to +7, with +4 being the predominant form and +7 being exceedingly rare).
Also, for the record, Rhodes is correct that weapons-grade plutonium is comparatively not very radioactive. There are five major isotopes of plutonium, with atomic weights from 238 to 242. Plutonium-239 is the isotope used for weapons production, and decays via alpha particle emissions, which means it's not really all that dangerous except internally, especially since it decays rather slowly (it's half-life is 24100 years). Notably, other than the spontaneous fission of Plutonium-240, all the isotopes except Plutonium-241 (which undergoes beta decay to Americium-241) only undergo alpha decay, and as such are relatively safe with minimal shielding (ignoring the high decay-heat of Plutonium-238 which is utilized to power RTGs).
Thanks for asking this question. I'd heard before that Pu was actually more chemically toxic than its toxicity due to its radioactivity, but had never followed up by checking out this claim in detail.
tl;dr: Plutonium is very safe unless you grind it up into dust and inhale it, in which case the hazard is probably from radiation, not chemical toxicity. There is probably no way of knowing for sure, because we don't know enough about things like the dependence of harm from radiation on the dose rate as opposed to the total dose.
I'm going to assume we're talking about 239Pu, which is what is used in bombs. It has a half-life of 24,000 years, and it decays via alpha emission to 235U, which is effectively stable (half-life of almost a billion years). Note that it doesn't decay by fission (that only happens in bombs), so comparison with nuclear fallout is not relevant.
To get a comparison of chemical toxicity to toxicity due to radiation, I think all we need is a very rough order-of-magnitude estimate of chemical toxicity. Organic mercury is extremely toxic (about 10 times worse than arsenic), and it has an LD50 of about 0.1 g, so that's probably a reasonable upper limit for any other heavy metal such as plutonium.
239Pu's radioactivity is in the form of alpha particles, which are only dangerous if emitted internally, because they can't penetrate the epidermis. The hazard then seems to me like it would depend crucially on how the internal exposure occurred. If you eat an alpha emitter, then it will stay in your body until it's either excreted or decays. The half-life for excretion of organic or metallic Hg is on the order of months, so that's probably a reasonable order-of-magnitude estimate for other heavy metals. On the other hand, there are people at nuclear weapons labs who do machining of plutonium pieces, and this kicks up plutonium dust. They do this machining inside glove boxes, and I assume the chips and dust are swept up very carefully. The dust can be breathed in, and microgram particles that get into your lungs are likely to remain there for the rest of your life (Lenntech, ATSDR 2010). From the lungs, it can also migrate to the bones or liver. ("Much less than 1%" of ingested Pu would do so.)
For internal exposure to alpha emitters, we have good data on 210Po, which was used in the Litvinenko assassination. The LD50 for this substance is believed to be about 1 μg. It has a half-life of 138 days, and although I don't know its half-life for excretion, as described above I'd guess it's on the same order of magnitude, so to within a factor of order unity, we can probably pretend that all of it decays within the body. But if you eat 239Pu, then assuming it gets excreted within ~100 days, its probability of decaying within your body is only about $10^{-5}$. Therefore we would expect the LD50 for ingested 239Pu to be on the order of $10^5$ times greater than that for 210Po, or 0.1 g. This is on the same order of magnitude as the chemical toxicity. Well, this would be of interest if any human being (or lab animal) were ever going to be exposed to this much of the stuff, and then maybe we would be motivated to work out the biochemistry in more detail, do studies, and so on. But in reality, nobody has ever eaten or will ever eat this much plutonium, so it's of no interest.
For inhalation, the balance shifts. If someone lives for 50 years after exposure and carries the dust in their lungs for that whole time, then the probability of decay within the body is $\sim10^{-3}$. That means that in terms of radiation damage, the LD50 should be about 1000 times higher than for 210Po, i.e., about 1 mg. This would make it about 100 times more toxic in terms of radiation than any plausible chemical toxicity.
You could argue that plutonium might be less lethal than implied by this estimate because a radiation dose that would be lethal if suffered all at once can be less dangerous or almost harmless if spread out over a period of years. This probably reduces the radioactive toxicity of plutonium by a big factor relative to the estimate above, but I don't think it can reduce it by a factor of 100, which is what we would need in order to make the radioactive toxicity comparable to any realistic level of chemical toxicity.
So to summarize:
For external exposure: Zero hazard from radiation, some hazard from chemical toxicity but probably no worse than the (very small) risk from external exposure to substances like lead or mercury.
Ingestion: Chemical toxicity is not relevant because nobody will ever ingest enough to be in danger. On a population basis, radiation could conceivably cause some excess cancers, but I doubt that there is very much unreacted plutonium in fallout, and the population risk does not seem to have been considered sufficient to merit discussion in Simon et al.
Inhalation: The hazard from radiation is probably 1-100 times greater than the chemical toxicity is likely to be, even if the chemical toxicity is as bad as organic mercury.
References
ATSDR 2010, "Public Health Statement for Plutonium," https://www.atsdr.cdc.gov/PHS/PHS.asp?id=646&tid=119
Lenntech Water Treatment Solutions, "Health effects of plutonium," https://www.lenntech.com/periodic/elements/pu.htm
Simon et al., "Fallout from Nuclear Weapons Tests and Cancer Risks ," https://www.cancer.gov/about-cancer/causes-prevention/risk/radiation/fallout-pdf
