Occupational exposure is a lot different than home exposure. People soldering on the job are doing so for hours a day, every day. You soldering as a hobby are not.

The dose makes the poison.

Of course, nothing is completely without risk, and an argument can be made that avoiding any avoidable risk is good, even if that risk is tiny. But the risk that comes from the fumes of soldering, unless you're doing it a whole lot, are much, much smaller than lots of risks you take every day without worry.

Everyone has a different risk tolerance. For instance, I intentionally use leaded solder because it works so much better than the lead-free varieties. But I'm cautious to avoid handling the stuff if I have any open wounds on my hands, and to avoid touching my face until I've washed my hands. That's an acceptable risk for me.

Your source isn't much of a source. It doesn't point to any studies that provide data that show that solderin is one of the leading causes of asthma.

Pity, I rather like the smell of that stuff.

If you're worried about lead just use RoHS solder?