Mmm.. actually, I just had a thought. I wonder if circuit "ground" is the cause. The TTL serial signals from the thermostat are relative to it's own "ground/earth" wiring, derived from one leg off the bridge rectifier.
Thinking about it now, I don't believe I've fried anything when the serial is connected a battery powered notebook computer, and I know for sure I've fried a ton of components when the notebook is on AC wall power.. with a house ground/earth.
I don't know much at all about how the AC supply from the furnace is wired, but it might have one leg hooked to house ground/earth, or at least have some hefty potential from earth.
Undoubtedly something to do with that.
Ethernet is fine of course, because it uses transformer couplings for the cat5e connections at both ends. But serial has a DC ground..
I'm putting an opto-isolator chip on the board now for the three serial signals. That should keep me from frying anything new.