Yes.
US consulate report on Saudi Arabia
Conversion from Islam to another religion is grounds for the charge of apostasy, which is legally punishable by death, although courts have not carried out a death sentence for apostasy in recent years.
The law requires applicants for citizenship to attest to being Muslim
The law deems children born to Muslim fathers as Muslim
State department
The U.S. government estimates that between 85 and 90 percent of the country's citizens are Sunni Muslims. Shia Muslims constitute 10 to 12 percent of the .
MEC
All Saudi citizens are declared by the State to be Muslims
ARDA
While accurate religious demographics are difficult to obtain, approximately 90 percent of citizens are Sunni Muslims, who predominantly subscribe to the Government-sanctioned interpretation of Islam. In the western Hejaz region, there are sizeable communities following other Sunni interpretations.
Ten percent of citizens are Shi'a Muslim
Cultural Atlas
Religion is a core aspect of everyday life in Saudi Arabia. It plays a dominant role in the country’s governance and legal system, deeply influences culture and daily life. The official religion is Islam, with the majority of Saudi citizens being Sunni Muslims (roughly 90%), typically following the Hanbali school of Islamic jurisprudence. It is estimated a further 10% of Saudi citizens are Shi’a Muslims.
ERT
while the native population is all Muslim (85% Sunni, 15% Shia) and
ethnically Arab. There is a small minority of remaining Bedouin desert tribes.
Additionally non citizens are required to carry religious identify cards
The government requires noncitizen legal residents to carry an identity card containing a religious designation for "Muslim" or "non-Muslim."
Saudi citizens are not required to carry that card. In a nation that legally treats non-Muslims differently (it follows an interpretation of sharia law which treats non-Muslims differently). This tells us something about how Saudi Arabia views its citizens.
Saudi Arabia has expelled non-Muslims from its territory.
70 years ago the city of Najran was conquered by Saudi Arabia. After a lot of persecution, the 600 Najrani Jews were allowed 1 day to leave, or they would "never leave again".
I interpret "or never leave again" to imply that those groups who refused to leave were buried in the sand. Their memory washed away by the wind.
Saudi Arabia barely, barely tolerates Muslims from a different sect as citizens. And the clash between the majority/minority population is quite vocal despite Saudi Arabia's censorship (and beheading of journalists)... I think an official non-Muslim minority citizen population would make the news occasionally.
Foreign Policy
Saudi Arabia still forbids the construction of Shiite mosques
UAB
textbooks used in elementary and middle schools stigmatize Shia beliefs and practices and go as far as to claim that Shia Muslims are disbelievers, suggesting that Shia should not be considered Muslims
newarab
senior Wahhabi clerics - who strongly influence the royal family - endorse execution by beheading for offences that include apostasy, adultery and sorcery. They also often describe Shia Muslims as heretics.
TLDR:
In Saudi Arabia you are Muslim if your father is Muslim. In order to apply for citizenship you must be a Muslim. And leaving Islam is punishable by death. More specifically you need to be a Sunnite.
Note: I am not saying that aren't Saudi Arabian Citizens who are secretly Christian, Buddhist, Atheist, etc., ... What I am saying is that such individuals keep that belief private and are careful to show up to the mosque every Friday.
