* Tens of thousands join rival pro-Kremlin and ant-war demos in Moscow
* Rallies comes a day before referendum on Crimea joining Russia
* Most Russians back President Putin's policy in Ukraine
By Maria Tsvetkova and Jason Bush
MOSCOW, March 15 (Reuters) - Russians took to the streets of Moscow in their thousands on Saturday to demonstrate for and against President Vladimir Putin's policies in Ukraine.
Crimeans vote on Sunday on whether to reunite with Russia after pro-Russian forces took control of the peninsula, triggering the worst East-West confrontation since the Cold War.
Most Russians strongly back Putin's actions and see Crimea as rightfully part of Russia. But a minority are horrified, fearing that Putin is risking war with another Slavic country formerly seen as a brother nation.
In a rally organised by a Russian Orthodox movement "in support of Crimea and against fascism", some 15,000 gathered on Revolution Square near the Kremlin, according to police.
Accompanied by a brass band playing patriotic marches, the well organised demonstrators, some waving Soviet hammers and sickles, chanted "Crimea is Russia", "We defend our own!" and "No to fascism!"
"We want to say a firm 'no' to the fascist junta that came to power in Kiev and therefore we naturally want to support our comrades in Ukraine," said Pyotr, one of the protesters.
But Saturday also saw the first big protest against Putin's policy, on Sakharov Avenue, site of the first large anti-Putin demonstration in December 2011, when tens of thousands took to the streets to protest against electoral fraud.
"I am ashamed for Russia and our people," said publishing company employee Valentina Legonkova, 69, who was carrying a Ukrainian flag although she is Russian.
"We are behaving towards Ukraine like swine," she said. "We will soon be on the level of North Korea."
Police said that around 3,000 people attended, but witnesses put the number at around 30,000, making it the largest protest for two years.
In the two weeks since Putin received parliamentary backing to deploy troops in Ukraine, Russia has seen dozens of government-backed rallies supporting the "defence" of Crimea. Smaller unsanctioned anti-war demos have led to scuffles with police and dozens of arrests.
"NO TO WAR!"
Saturday's protest was authorised, however. There were Ukrainian and Russian flags as well as EU flags like those carried by pro-European demonstrators in Kiev's Maidan square.
Some chanted "Glory to Ukraine, glory to the heroes!", a slogan also borrowed from Kiev, others "Down with Putin!", "No to war!", "No to fascism!" and "Russia without Putin!"
One placard read: "Hungary 1956, Czechoslovakia 1968, Ukraine 2014", likening Russia's actions in Ukraine with the Red Army's suppression of east European reform movements in the Cold War.
"My duty is to show support for the Ukrainian people in its desire to live independently from the dictatorship of the elder brother," said Moscow teacher Irina Seseikina.
The protest taps into a wider vein of discontent, strongest among the Moscow middle class, who are also appalled at rising corruption, political repression and censorship under Putin.
But so far the Ukraine crisis and last month's spectacular Winter Olympics in Sochi have solidified broader support for Putin, whose increasingly nationalist and conservative agenda plays well among Russians nostalgic for the Soviet Union.
His approval rating now stands at about 70 percent. Meanwhile, in a recent poll by the independent Levada Centre, two-thirds said they believed that not only Crimea but also mostly Russian-speaking eastern Ukraine were "in essence" Russian lands.
"Sevastopol means for Russia and for the Russians much more than the Falklands mean for England. But England didn't give the Falklands up and went into a big war, right?" said Captain Alexei Ryabtsev, a pro-Kremlin demonstrator.
Russia's largely state-controlled media have pushed the Kremlin's view of the revolution in Ukraine as an anti-constitutional coup by fascist extremists with Western backing.
Few of the anti-war marchers had any expectation that their action would make a difference.
"These images are for the evening news, which will talk about a (subversive) 'fifth column'," said Alexander, a teacher who declined to give his last name.