I've had a stall warner go off on approach in a PA-28, woke me up a bit.
It was just gusts, speed, attitude was fine but I remember well pushing down a little and opening the throttle before checking the airspeed.
Vintage taildraggers in my tiny experience are something you never completely learn, you never get complacent, you never ever stop being taught by them that they can bite. I'm still a fair way off taking up passengers in one though.
In all it's your judgement. On the one hand I've flown with people who I had doubts about up to the point where they really scared me. On the other a slightly off departure in a crosswind happens at times in taildraggers especially when you haven't yet developed a feel for the type. My question would be should one be carrying PAX though, probably not the best judgement call but I've heard of much worse attempts at departure. Nothing makes you want to be in the air like
now more than a older tailwheel plane in the take-off run with a gusty crosswind.
If I had experienced either in a Cub for example as a PAX it wouldn't necessarily put me off flying with the pilot again. They are very much 'feel' aeroplanes and sometimes it's practically impossible to get useful information out of the instruments in gusty conditions and one has to fly by attitude and feel.
I'm not a professional pilot either, hopefully as a PPL who has dipped their toes in vintage tailwheel and become addicted, my thoughts are helpful from the perspective of someone with knowledge of flying as PIC but also as an at times concerned passenger. In all if you keep feeling uncomfortable at some point you'll simply stop enjoying flying with that pilot, though the reasons here are forgivable IMOH.