It's a great question Bud & one that can get some good answers and some misinformation.
Hopefully someone who pours plastics will provide their views and experiences. I've only poured lead and have been doing it a long time.
There is already some information posted here, but I'll add to it.
For the most part with lead, burns or lead oxide will be the most serious potential hazards. Lead oxide dust in the air is also a potential source for possibly lead poisoning, but when lead is poured in a well ventilated area, even that potential hazard can be limited.
Elemental lead is not toxic, although you will read that it is. It's not soluble and cannot be absorbed through the skin. If it is ingested, it can become toxic, as acids in the digestive system breaks it down, so the simple solution is to not ingest it. Never use utensils for pouring lead that are also used for food prep. Never pour lead in a kitchen, and don't eat or drink in an area that is used for pouring lead. These should be common sense.
Lead oxide, which is that nasty gray, dust like coating that gets on lead, is soluble, can be ingested, absorbed through the skin when moisture is present, and has the potential for inhalation and is toxic as a result. But again, limit it and the potential for a health problem is also limited. Always wash your hands thoroughly after handling lead. It's not usually absorbed through the skin of the hands & fingers, but through softer tissue, and over a longer time period of exposure. Most lead related health issues are due to exposure over a long time frame, which has been the case with such exposure when lead was used in automotive fuels and paints. The adult human body can remove lead in a short term exposure without ill affects.
Most folks when they have a serious issue when pouring lead is from burns since lead has to be heated to 621.5 degrees F, the melting point, to get it into a liquid state so it can be poured into molds. Wearing leather gloves and other protective clothing helps limit that problem. I have a leather welders apron that i'll wear, in addition to the gloves.
It is often stated that vapor from lead is a potential health hazard, this is true, but since the vapor point of lead is very high, when using melting equipment that is typical for pouring fishing tackle, the temperature should never get even close to that. The boiling point of lead is over 3100 degree's F. If melting lead with gas type of heat sources, such as propane, MAPP or acetylene gas, it's certainly possible to get the temperature up that high, but most folks use electric melting equipment which have controls that limit the heat, and the lead temperature should never reach the vapor point. The lead only needs to be molten to pour it, so it makes little sense to heat it that hot.
One very serious potential hazard with lead is moisture. One drop of water introduced into molten lead can cause an explosion. It's not an explosion in the sense of a combustible material, but similar affect. With the lead temperature at over 600 degree's, the water expands into steam so rapidly, that it literally blows up the lead in a melting pot, and the result sprays the hot lead as the steam tries to escape. I've had it happen once and that was once too many. Fortunately, I was wearing that leather apron, gloves & a face shield at the time, so only got a few minor burns as the hot lead was sprayed on my shirt sleeves. I was also wearing a long sleeve shirt. One single drop of sweat, can cause a big problem, so keep anything liquid away from molten lead.
One other potential hazard with lead would be when recycling used lead. It would depend on the source, but some lead materials may have various substances on them. Wheel weights are a good example. I've melted down lead wheel weights for years, and grease, oils, dirt, paint & even rubber can be on them. if it's not cleaned off prior to melting it often burns and creates hazardous fumes. That type of procedure should always be done outdoors in an open area. There is too, always the potential of trapped moisture. I've got into the habit of placing lead that has to be recycled into a oven which I use for powder painting, to make sure any moisture that might be trapped is evaporated prior to melting it down.
For that matter, lead pouring should always be done in an area with good ventilation. I pour in my garage, just inside the doorway, and always with the overhead doors open, and never use anything but clean ingots. I still melt down scrap lead when I get it, but always outdoors. I have a respirator that I'll wear if there's anything on the lead I'm using and it has filters that are rated for lead dust & vapor.
I've been pouring for well over 45 years, and have had my blood tested for lead when I've had physicals. I've never tested positive. Lead for fishing tackle can be safe to use, as long as folks are aware of all the potential risks and take the necessary precautions.