Even taxiing out when a storm gust front hits should make you thinking that parking (wherever Ground suggests) and shutting all engines down is the thing to do, if a return to the gate seems impractical-we have done this more than a few times and it sure saves lots of fuel-we can't afford to kid ourselves about fuel or weather. If there is a fairly strong small thundercell on the approach or departure path, (or even near another runway!) you are really pushing your passengers luck quite far to even try it-never mind your safety record, reputation and career. Would you want your family on such a plane, even if it is flown using FMC/VNAV/LNAV/autothrottle by the most famous national carrier, whose flight crewmembers wear shiny stripes and FAs beautiful, colorful scarves? On a 15-mile final into Raleigh-Durham, NC last summer we noticed the weather getting stronger just to the left of the localizer for runway 5R, but not much radar contour. The line was not solid and not very wide. But even though there were NO large cells right by the airport or by us, the turbulence was becoming constant moderate and we both had an uncomfortable feeling about the rest of the approach-so we spoke up about it and came in from the other side after delay vectors downwind of it, and in the opposite side (ATC suggested this). I broke off an approach in Albany NY simply because of a slight tailwind on ILS approach to the north, well aware it was a wet, short runway (to hell with the schedule). Came in on opposite ILS when mild rainshower went by. Sometimes even wind readouts are not accurate.
Just say something to the other pilot(s), that you don't like the way it looks and/or feels-no matter which seat you are in, even if you are the FE! Don't be silent about an uncomfortable "feeling". It is such silence which can lead to incidents or tragedy, but guys don't want to admit it as often as the lady pilots.
A few years ago, there was a huge cell on the radar, contours or not, barely north of IND airport and we broke off the 25-mile long localizer final and diverted straight to Louisville. It must have grown very fast! Even if we had flown to within a few miles of the airport in mild winds, once we are near the ground and a microburst comes down or a gust front blows out, it could easily be too late and low for recovery. Check previous (NTSB reports) accidents in the US near thunderstorms. Just offhand, I am reminded of JFK, Charlotte/MSY (DC-9), New Orleans/MSY (727), Dallas-FW/DFW (1011): read the FE's remarks about his nervous legs when they entered the turbulence, a few minutes before the crash...). If you really do not like the look, feel or sound of something, this is NOT the time to be like a kid in school, afraid to raise his/her hand to state a problem. A pilot many years ago told me that years before in southeast Asia, he was spit out of a storm almost upside down in an Air America (or CAT?) DC-3, and was one fine pilot when I knew him. Caramar, Delaware Corp, Doublecheck...