As I've picked on Qatar a little too often, here's the much-milder but still religious supremacist Jordan. Non-muslims are legally discriminated against to this day in Jordan, one of Israel's neighbours:
Islam is the State religion. The King must be Muslim and the law affords primacy to sharia law.
Authorities may prosecute individuals who proselytize Muslims under the penal code’s provisions against “inciting sectarian conflict” or “harming the national unity.” Both offenses are punishable by imprisonment of up to three years or a fine of up to 200 dinars ($280).
Islamic religious groups are granted recognition through the constitution and do not need to register with the government. Non-Islamic religious groups must obtain official recognition through registration.
Recognized non-Islamic religious groups are tax-exempt but do not receive the government subsidies granted to Islamic religious groups.
Religious groups not recognized as denominations or religious entities lack legal status and may not undertake basic administrative tasks such as opening bank accounts, purchasing real estate, or hiring staff.
The government also refers to the following criteria when considering recognition of Christian groups: ... its religious doctrine must not be antagonistic to Islam as the state religion;
Sharia courts do not recognize converts from Islam as falling under the jurisdiction of their new religious community’s laws in matters of personal status. Sharia court judges may annul the marriages of converts and transfer child custody to a Muslim nonparent family member or declare the children “wards of the state” and convey an individual’s property rights to Muslim family members.
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marriages between a Muslim woman and a non-Muslim man are not permitted; the man must convert to Islam for the marriage to be considered legal.
In accordance with sharia, adult children of a man who has converted to Islam become ineligible to inherit from their father if they do not also convert to Islam unless the father’s will states otherwise.
Per the ban on conversion from Islam under sharia, converts from Islam are not allowed to change their religion on electronic records.
Jordan - United States Department of State