Is it permissible for a Muslim monotheist to eat from the meat bought by his family from the market, when they are not monotheists?

Avoiding meat slaughtered in Muslim countries, under the pretext of not knowing the slaughterer, is an act of excessive scrupulosity and fanaticism. The meat slaughtered by Muslims is permissible to eat unless their disbelief is proven. A Muslim's action is presumed to be sound unless proven otherwise. The default rule for slaughter in Muslim countries is permissibility. If the majority of the population in a country are Muslims, then it is permissible to eat, acting upon the غالب (predominant situation).