Do people take birth in other religions by Allah's will?
Is it by Allah's will that people of other religions exist in such large numbers?
Or is it against Allah's will that this state of affairs exists and continues?
In Quran, (Surah Maida - Chapter 5, Verse: 48) God has mentioned that
...Had Allah willed, He would have made you one nation [united in religion], but [He intended] to test you in what He has given you; so race to [all that is] good. To Allah is your return all together, and He will [then] inform you concerning that over which you used to differ.
So different religions are in complete accordance with His will. Rather, forcing everyone on a single religion is against His will
It doesn't matter who your parent or family are. In Islam everyone is born a Muslim. Every baby you see is a Muslim however when some grow up and decide to follow other faiths when he knows Islam is right then he will be punished. Religion is not something that should be blindly followed by what your family follows but what the truth is. And of course everything happens by the will of Allah. People of other religions exist because Allah guides whom He wills.