Ive never asked a woman what she thinks, but i have my own negative opinion of a "whale tail" (the triangular, centered T at the top of a thong above the buttcrack) and i think granny panties are equally as lame.
From recent posts on reddit, it seems like most women find them utilitarian or are basically indifferent to them. You can always say that you just had a vasectomy and that its doctor's orders.
There is also the option of wearing an undershirt (white tee or wife beater) beneath your other shirt to keep yourself tucked in and less backside reveals.
Dance to your own drum, man, and rock that jock. You may want to start with athletic brands (bike, duke, mcdavid, etc) before wearing fashion brands- those do seem to convey a different message.