Depends who you ask, you’ll get a lot of different answers (except for this thread I guess). Flux fumes are harmful to breathe, and lead is toxic.

Even though there are many people who might say it’s fine to do on occasion, my personal risk tolerance is low. With that said, I solder in front of an open window with a charcoal smoke extractor and a fan pointed out the window. The idea is that the fumes get filtered through the charcoal, and whatever remnants are then blown outside by the fan. It’s cheap and the filter thin, but it’s better than nothing and I’ve never regret spending money on things to keep me healthy. I’ve seen many lungs of people who smoke, who have lived in polluted areas, etc and I have no desire to end up like them with my lungs looking like a dusty gross heat sink. My personal rule is, if I can’t have that window open and fans going, I don’t solder inside.

After soldering I make sure to wipe down my work table and thoroughly clean my hands with soap and water to get rid of any lead before touching anything else in the house, and especially before eating or drinking. Lead is more toxic to your body, so this is non-negotiable. This is doubly true if you are working on CRTs, with the risk of being contaminated by mercury, which is probably info you already knew going in. Still it cannot be overstated - an ounce of prevention is worth a pound of cure.