* Saudi designation of Brotherhood divides Gulf Arab bloc
* Uncertainty over impact on Brotherhood supporters
* Islamist groups part of politics in Kuwait, Bahrain
By Yara Bayoumy and Sylvia Westall
DUBAI/KUWAIT, March 12 (Reuters) - Saudi Arabia's fierce campaign against the Muslim Brotherhood, already on the run in its Egyptian birthplace, has divided a Gulf Arab bloc, causing discomfort in some member states where the Islamist group is embedded in daily politics.
Feuding with Qatar over Islam's place in a turbulent Arab world, Riyadh recalled its ambassador from Doha last week and branded the Brotherhood, a Qatari ally, a terrorist group.
Saudi Arabia has swung firmly behind the Egyptian military, which deposed President Mohamed Mursi last year after mass protests against the Brotherhood leader. Riyadh has since pumped billions of dollars into Egypt's creaking economy.
Punishing Qatar for its pro-Brotherhood stance shows a new Saudi confidence in pushing its agenda, even if it means splits in the six-nation Gulf Cooperation Council (GCC), a U.S.-aligned alliance which usually keeps any internal tensions private.
Bahrain and the United Arab Emirates have followed Riyadh's lead in recalling their envoys from Qatar. But Kuwait, home to an active community of political Islamists integrated into the political and business elite, has voiced disquiet and offered to mediate in the dispute.
Oman, which has opposed plans for a closer Gulf union, appeared to downplay the seriousness of the rift on Wednesday.
"What happened is nothing more than differences and friendly reproach between brothers ... what happened is not a divorce," the Arabic-language Oman Daily cited the Minister of State for Foreign Affairs Youssef bin Alawi bin Abdullah as saying.
The UAE shares Saudi Arabia's view that the Brotherhood, with its taste for populist electoral politics, poses a threat to dynastic rule and to Gulf security, but no other GCC member has yet declared it a terrorist organisation.
Bahrain may be politically close to Riyadh, but Islamist sympathisers are among those who support its own Sunni ruling family against challenges from the island's Shi'ite majority.
Kuwait must also tread carefully if it is to avoid fuelling chronic strife pitting its hereditary rulers against political opponents who include conservative tribal leaders and Islamists.
"The Saudi announcement is likely to complicate relations with Gulf allies, especially against the backdrop of escalating tensions with Qatar," said research analyst Wafa Alsayed of the Bahrain-based International Institute for Strategic Studies.
"(The terrorist listing) really complicates things because it means anyone could be directly or indirectly subjected to these laws, and someone could be arrested so easily," she said.
Saudi wariness of the Brotherhood dates back at least to the 1990s when some Saudi leaders accused it of inspiring the Sahwa opposition movement agitating for democracy in the kingdom.
The Saudis are fuming over the pro-Brotherhood sympathies of Qatar, which appears happy to act as a catalyst in the rapid changes shaking up Arab politics since the uprisings of 2011.
The Brotherhood's acceptance of the ballot box challenges the Gulf tradition of dynastic rule, offering an alternative interpretation of the role of Islam in politics.
Many Gulf states also place little credence in Brotherhood protestations that it is a non-violent movement.
All of which makes political Islamists in the Gulf uneasy.
It was not possible to reach any Saudi Brotherhood figures who generally keep a low profile. But sympathisers elsewhere in the region expressed apprehension.
Mohammad al-Dallal, a Kuwaiti Islamist and former lawmaker, said he believed the Saudi actions were part of a coordinated policy with Egypt to eradicate the 86-year-old Brotherhood.
"It is a strange thing, because the Muslim Brotherhood is not a terror group and they are not a violent group, especially in the GCC countries," Dallal said, noting that Gulf groups sympathetic to the Brotherhood have not adopted its name.
Political Islamists in the Gulf are puzzling over what the Saudi decree means in practical terms, at a time when the kingdom is toughening penalties for terrorism.
The decree forbids anyone from supporting organisations ... "or showing their affiliation, or sympathy or holding meetings under its umbrella, whether within the kingdom or abroad".
Saud al-Sarhan, director of research at King Faisal Centre for Research and Islamic Studies in Riyadh, said the edict was unlikely to affect Saudi relations with Gulf neighbours where the Brotherhood is part of political life "as long as they (the Brotherhood) are not trying to interfere the Saudi internal policy or trying to create instability in the region".
Saudi Arabia, Bahrain and the UAE said they had acted against Qatar because it had reneged on a GCC agreement not to meddle in the internal affairs of member states.
Qatar denies this, saying the dispute is rooted in wider Middle East disagreements, such as its policy on Egypt.
All the GCC members may be uneasy about a rift that violates their cherished goal of political and security solidarity, but Bahrain appears to be in the most awkward position.
Saudi Arabia and the UAE have helped Bahrain combat Shi'ite-led protest and demands for more democracy since 2011. Bahrain's Sunni Islamist groups, such as al-Minbar and al-Fateh, have mostly sided with the government against the Shi'ite opposition.
"Bahrain is in a very complicated Catch-22," said IISS's Alsayed, arguing that its rulers had a special relationship with Saudi Arabia, but also relied on political support from their Sunni constituency. "Which one matters more?"
A Bahraini lawmaker, who declined to be named, criticised the Saudi designation of the Brotherhood as a terrorist group.
"So are the Brotherhood now going to be treated like al Qaeda? Despite our differences with the Brotherhood .... this comparison is unfair," said the lawmaker, who belongs not to the Brotherhood but to the ultra-orthodox Salafi trend.
"I think in Bahrain it would be very difficult to give the group this designation because there is no evidence that the Brotherhood in Bahrain is tied to terrorism. They are citizens who denounce terrorism," he said.
Islamists in Kuwait who share the Brotherhood's ideology, such as members of the Islamic Constitutional Movement, often write in leading newspapers and appear on television channels.
Also active in the private sector and the law, they form an important opposition group, though their influence has waned since late 2012 when most of them boycotted a parliamentary election over changes to the voting system.
It is an open question whether Kuwaitis and Bahrainis who belong to groups tolerated at home would run the risk of arrest if they travel to Saudi Arabia or beyond.
Dallal said the Saudi decree would make it difficult for individuals to speak favourably of the Brotherhood for fear of retribution. It might even exclude people seen as linked to Brotherhood from going on pilgrimages to Mecca in the kingdom.
"You cannot even speak with human rights organizations, according to this decision," the Kuwaiti Islamist said. "You cannot really participate in any conference, internationally." (Additional reporting by Rania El Gamal and William Maclean in Dubai; writing by Yara Bayoumy; editing by William Maclean and Alistair Lyon)