The Permanent Committee for Scholarly Research and Ifta' consisting of the Mufti Abdul-Aziz ibn Abdullah Al Al-Shaykh, Shaykh Salih Al-Fawzan,(May Allah preserve them), Shaykh Abdullah ibn Ghudayyan and Shaykh Bakr Abu Zayd (May Allah have mercy on them) answered a similar question. The complete answer and verdict can be found here.
Islam came into being to remove Shirk (associating partners with Allah), idolatry and polytheism. Make no mistake, the ultimate crime according to Islam is Shirk.
Allah says in Qur'an:
Indeed, the religion in the sight of Allah is Islam.
And He says :
And whoever desires other than Islam as religion - never will it be
accepted from him, and he, in the Hereafter, will be among the losers.
Now, the Kingdom of Saudi Arabia adopts Islamic Shariah as the law of the land. How can you expect something that encourages disbelief to be constructed in their land? It is the Islamic duty to forbid disbelief. Hence, the public worship of anything other than Allah is forbidden. What you do in private, however, cannot be monitored. The least that can be done is prevent construction of churches, temples and so forth. Because they promote disbelief and apostasy is a crime punishable by death under Islamic Shariah which is carried out by the legal authorities in the country.
So a good analogy would be - If cocaine is banned, how logical would it be to legalize cocaine selling shops?
Apart from this, unlike everyone says here, there is a hadith to support this action:
The Prophet (peace be upon him) stated:
There should not be two religions together in the Arabian Peninsula. [Al-Muwatta, vol.2, pg.892, Narration of Aishah (May Allah be pleased with her).]
Thus, scholars have unanimously agreed upon the prohibition of building temples such as churches in Muslim countries. They have also agreed that there is an obligation of destroying churches and any other places of worship if they have been recently built.
Allah says in Surah Al-Maidah:
Help you one another in Al-Birr and At-Taqwâ (virtue, righteousness
and piety); but do not help one another in sin and transgression. And
fear Allâh. Verily, Allâh is Severe in punishment