The native, citizenry body of Qatar are all Muslims and conversion to another faith is illegal. However, like other Arabian countries, much of the construction, hospitality, and tourism industry work is done by guest workers from countries like the Philippines, India, Eastern Europe, and Indonesia/East Timor. (Treatment of guest workers ranges from standard to nearly slaves) Some of these workers are Catholic and the guest worker program has boosted the Catholic population in Arabia to a stunning 1,300,500. Previously they had to worship in secret or in a limited public capacity.
With the establishment of the church Qatar takes another leap forward into the globalized world. Qatar allows women to vote and its increasing liberalized personal/religious laws are beginning to catch up with the likes of Bahrain and the United Arab Emirates.
There is an antipode to the liberal tri-Arab axis: Saudi Arabia. Under the strict Sharia guidance of the Committee for the Propagation of Virtue and the Prevention of Vice, religious freedom in the Kingdom is not permitted. Catholics and other non-Sunni groups are forced to worship in the shadows. Churches, temples, synagogues are not permitted. Conversion is punishable by death. Enterance of a non-Muslim into the cities of Mecca and Medina is also punishable by death. Prince Turki bin Faisal al-Saud invitation to the Kingdom is not entirely welcoming.
Saudi Arabia is under a Wahhabi religious regime which is revolutionary expansionist. The Wahhabi's are currently focusing their efforts with spreading their creed in Central Asia, Europe, and the more radicals are supporting the fight against Iraq and Afghanistan. These diversions have helped to allow liberal forces to open up the tri-axis to the rest of the world.
The axis and Saudi Arabia have a bit of give and take going on right now. Qatar, the more moderate of the liberal three, is tempered by the fact it is a weekend getaway place for many Saudis. But the liberal ways of the axis are seeping into the Kingdom too. While it was extremely limited, local elections have been held in which a wide array of candidates were elected to office. And some universities are allowing women to attend. Finally, women no longer need the permission of their husbands to leave the Kingdom on vacation- any close male relative will do.
One external event will impact the liberalization or Wahhabization of the Arabian peninsula: the War on Terrorism. If the Coalition can finish the job they started and build up a stable, democratic Iraq then the conservative countries will be pressed by liberal countries on two fronts. If al Qaeda in Iraq is victorious in creating a chaos state then the momentum will be with the Wahabbis and Islamic fascists will bring the fight against their liberal home countries. If the Shia militias backed by Iran can make Iraq a Shia satellite state then the future of liberalization is up in the air. Iran is liberal in some respects while being oppressive in others.
Time will tell.