I can get why the FBI may be drawn to Mormons, but I also wouldn't be surprised is the Mormons actively encouraged their members to get jobs with the FBI.
I'd say the high level of education, pro-work, pro-patriotism, high morality emphasis on top of the extra level of foreign language competency makes it a natural fit.
I was surprised to find out recently my Dad had applied to the CIA back in the 60s- but on reflection not too surprised. The more the 60s and 70s went counter-culture, the more that the Utah/AZ/Idaho axis of Mormons went from their traditional pro-Democratic post FDR base to a pro-government pro-Republican, anti-Communist direction.
He ended up going into business instead, but if his background check hadn't gone on so long, he'd likely would have taken a .gov offer if it'd come before his corporate offer.