The problems in Greece are basically about financial politics within the Euro-Zone. It doesn't have a lot to do with US policy at all. German and French banks have invested money in Greece. A lot. And then rating agencies have rated Greece down. And that caused a financial down-break. Now German and French government want the Greek to pay it by ruining their national finances in a saving program. Ruining the retirement and social funds of the country and rising taxes. But Greece is actually bankrupt. The income of the state is lower than the interest rates. And the Greek don't want to stand up for the mistakes that Greek large companies and foreign banks made. But fears are that a state bankruptcy would destabilize the Euro currency.
Safe as ever.
As long as you steer clear of demonstrations with heated atmosphere and don't throw objects at Greek politicians or policemen. (And as long as you don't wear a shirt that says you like the IMF and Angela Merkels and Nicholas Sarkozys EURO-zone financial politics.)
People have attacked their own parliament members as well as policemen who protect them. Thrown stones and bottles and the like. So you don't want to get caught between the lines there. But no one has yet randomly attacked tourists or other folks. And it's probably not gonna happen.
even though they don't agree with 'our policy'. Seriously? How self-absorbed does one have to be in order to believe another country has to follow their policy?
I would say it's pretty safe, even though they don't agree with our policy and such I wouldn't say they would bother with a tourist.
If it was really unsafe, your embassy would issue a travel alert, I'm sure its safe, but common sense is still recommended