Lead-based solder is preferred for high-reliability electronics (space, nuclear, military, etc.) because it’s easier to rework, easier to verify by visual inspection, and it’s not vulnerable to tin whiskers.

Here’s the relevant safety guides from Stanford and MIT.

In short, if you do a lot of soldering, there are long-term occupational hazards from both lead oxides and rosin. Both guides agree that the main hazards are the fumes (workstation should have a fume extractor or suitable filter) and residue on your hands (wash hands with soap and water before eating).

I couldn’t find any numbers on how much material is removed by washing, but every reference emphasized that soap and water are vitally important.