To be fair, they are right. It's pretty nasty stuff. If you breathe it in or ingest it in any way that is. Neither of which happens when you're soldering unless you're one of those idiots that licks the solder. The issue is however with the production, disposal and recycling. Historically stuff, including discarded electronics, were buried in landfill as part of general waste and made it into the water table eventually. This has quite devastating health effects for potentially hundreds of years and has been proven to cause developmental issues[1]. Mishandling it can be quite bad too [2].
Fundamentally the only way to prevent it appearing in landfill and general waste is to stop it being used in the first place. Batteries and roofing materials already have specialist handling facilities separate from general waste.
Stuff we build is likely to end up in the WEEE bins for disposal these days in the distant future but a lot of people just chuck any old crap in the bin and don't care what it is or where it's going.
[1]
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1257652/
[2]
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2897224/