But looking at the amount of rosin that I collected daily cleaning the suction tool of my Iron, I guess smoking tobacco is just as healthy.
I don't know if you're a smoker, know one, or have paid attention to cigarette ads - but it used to be common to advertise cigarettes in terms of "contains low tar".
What is "tar"? Tar is a gooey (and generally foul smelling) substance left behind by incomplete combustion of organic matter. Typically, its a part of smoke; when organic matter (particularly resinous plant matter) is heated and burned, the hot smoke contains gases which, if cooled, leave behind this substance. In the case of cigarette smoke, the majority of cooling happens inside the mouth, throat and lungs. Knowing how gooey and ugly the substance is, that isn't a good thing. If you can cool the smoke or filter it in some manner (ahem - in a hookah or bong), a lot of the tar will be left behind, leaving you with a "smoother" smoke, and less irritation to the lungs.
So - what does this have to do with flux and resin?
Well - that stuff is usually made from plant materials (pine resin is common), then generally mixed with solvents and waxes to form the paste used. When it is heated in soldering, the fumes and smoke you get are composed of that resin being vaporized. If you could cool it off, you would then get back the "tar", similar to what is in cigarette smoke. So - I wouldn't advise breathing it, but it probably isn't going to kill you instantly or make you grow a third eye, either. You would have to inhale a lot over a long time to see significant detriments to your health (likely shortness of breath, coughing, congestion - things of that nature - which would clear up over time once you limited your exposure again).
A couple of other things - the stuff called "pitch" or "pitchblend", which was used for sealing wooden ships way-back-when, was typically pine tar (although other woods were used as well), made by burning wood, then condensing the smoke. Road tar is a byproduct of the petroleum industry, made by the cracking of petroleum (basically, heating raw crude until it boils and vaporises, then cooling those gases in a fracturing tower - essentially a really large distillation system - the lower down the tower, the thicker the product, with the tars on the bottom; the next level up is basically diesel and kerosene). There's also tar made from coal (coal tar is used in a variety of medicinal preparations - one of the more common being dandruff shampoos). Finally, the black substance that forms on the inside of meat smokers and barbeques is "tar" from the smoke (from the wood or charcoal) that condenses on the inside surfaces of the cooker.
So - all in all, the smoke from flux (which is made with rosin) shares quite a lot with the smoke from other sources; I wouldn't say its healthy to breathe, but I wouldn't fear it like death, either, unless you happen to be asthmatic, have pneumonia, or other breathing issues, of course...