Got on a plane in JFK the other day and there was an overpowering wet dog smell. It was raining and we thought it was just wet carpet or something. The #1 had some perfumey spray she used to try and cover it up... point being, none of us were overly inclined to yell “fumes”— we just though the plane smelled bad. When we started the APU the smell got stronger and you could feel your lips tingle and very slight respiratory irration. Shut down APU, call MX, defer APU, #3 has headache and gets replaced. Huffer start, pushback, smell and irration returns, calls from cabin, return to gate, write up “fumes”, etc. When inflight sups came to plane, they remarked on the smell and how it gave them a headache and they were onboard for maybe 30 secs and packs were off. We talked to CPO, felt well enough to continue, got a new plane, new FAs and continued trip. Just because we weren’t taken off in stretchers doesn’t mean toxic fumes are a fairy tale. One short exposure may not be enough to cause noticeable symptoms, but what are the cumulative effects over years and years?