All perfect praise be to Allah, The Lord of the Worlds, and may His peace and blessings be upon our Prophet Muhammad and upon all his family and companions.
There is no harm in eating cheese made in western countries, and a Muslim isn`t required to trace the source of the rennet used in its (cheese) making since, in principle, their food is lawful, as Allah, The Almighty, said{what means}: "The food of the People of the Book is lawful unto you"{Al-Mai`dah, 5}. "
It is allowed to eat cheese made with rennet of an animal fed with other than milk since banning that increases difficulties on people while there is a maxim in Sharia that says: " Difficulties demand facilitation."{Nehayat Al-Mohtajj, 1/245, Al-Imam Al-Ramli}.
In conclusion, it is allowed to eat cheese made in western countries since Abu Dawoud reported that Ibn Omar narrated: " The Prophet (PBUH) was brought a piece of cheese in Tabuk. He called for a knife, mentioned Allah's name and cut it." However, if it was found out that the rennet was extracted from a dead animal or an animal unlawful to eat, then it isn`t allowed to eat the cheese made with it. And Allah knows best.