The fuel for a nuclear weapon is not particularly radioactive. If it were, you'd have to replace the fuel every once in a while to be sure that you can still make it go supercritical.
The fuel for nuclear weapons is chosen because it has high neutron-induced fission cross sections, which don't necessarily correlate with their activities.
So the real radiation risk comes not from handling the fuel, but from being around it when it goes critical or supercritical. Because then, the neutron population multiplies exponentially (neutrons are a particularly nasty kind of radiation), and a lot of energy is released into the surroundings.
If the weapons are handled properly, they should be kept subcritical at all times, until they're very rapidly made supercritical, and the explosion happens.
Plutonium is pyrophoric (it can ignite in contact with air), pretty reactive from a chemical standpoint, and toxic if it gets inside of you. So to keep it from corroding or posing a hazard to weapons workers (or the weapon itself), it tends to be electroplated with a thin layer of something non-reactive like nickel or silver or even gold. Properly handled, it is not so radioactive that it poses a major problem; the type of radioactivity it has (alpha particles) is bad _if_ it gets inside of your body, but your skin can block it. Plutonium poses a health problem if it is aerosolized (inhaling it is _bad_) or if particles of it get into the food supply (e.g. a contamination problem). You can hold plated plutonium in your bare hand — it is warm to the touch.
Uranium is less reactive and less toxic than plutonium. You can hold raw uranium metal (it is a heavy metal and still somewhat toxic, similar to lead, so you should wear gloves or wash your hands if you do handle it). The fuel in the bomb dropped on Hiroshima did not have any special plating on it for health reasons; it did have a small amount of cadmium (a neutron absorber) coating its surfaces, because they didn't want the bomb to go off prematurely (the weapon design was less efficient and more problematic in this respect).
>I guess my vision of nuclear material is that it’s kinda like pure acidic material thatis strong enough to tear through any metalthat is trying to hold it, but that is seemingly not the case. It just seems like something so potentially dangerous that I wouldn’t dare go near it, no matter what it’s stored in.
That's not a particularly accurate description of the properties or danger of radioactive material. With radioactive material, the main danger is from the released radiation, which is carcinogenic and also immediately toxic in very high doses. Beta and gamma radiation will penetrate various materials and can be risky to be near, but it is still a matter of concentration. You are constantly exposed to similarly energetic radiation from space (and much more energetic radiation even) but because the amount of radiation is so low the risk is also low. I.e. the individual particles (or photons) may be very energetic, but there are few of them. The same is true for any exposure to radioactive material on earth. If the dose of radiation you receive is low, for example because you were only exposed for a short time, the risk is low. While the radiation does penetrate material, it is not "infectious" as often displayed in media (with the exception of neutron radiation). Imagine it like a poison that can kill you at a distance instead of with direct contact only. The right type of container can reduce the distance, but otherwise, getting near radioactive material is not much different from being exposed to another carcinogenic toxin like cobalt.
Neutron radiation is a bit different, because it can cause radioactivity in material. So, getting exposed to neutron radiation increases the long-term risk because of this secondary radioactivity, but other than that there's not much practical difference. It would not, for example, turn you into a danger to others, any radiation strong enough for that will very quickly kill you.
Plutonium and Uranium aren't that radioactive.
Quick cheat sheet to tell how radioactive something is.
Look up the element - look at the isotope list
Pu-239 - half life is 2.41×10^4 years and it's byproduct is α - an alpha particle (its a helium nucleus) isn't "bad" it can be stopped by a sheet of paper or plastic film. But they are really bad if ingested - so don't lick Uranium or Plutonium.
The longer the half life, the less "bad" it is
Plutonium 241 has a 14 year half life and it emits beta radiation which is more penetrative than alpha