Obviously, this line can be drawn lots of places.
As a general principle: If it’s about YOU doing something for someone else, it’s fine. If it about you trying to get the government to do something for someone else, it’s political. If you are educating people on an issue, the focus should be on what the people can do themselves, not what the people can force the government to do. And such education should not be a lay service.
Political Activities-- All of which are just fine if done as individuals. Please try not to do these as/within congregations or in the name of UUism. (e.g. Your banner that says "Unitarians for Peace" will not be nearly as effective as the same group marching with a banner that says something more like "Mainstream folks for peace.")
Handing out petitions at Coffee Hour
Speculating about what religious figures would think about politics today, especially from the pulpit
Organizing trips to protest marches or letter writing campaigns.
Donating money to political groups lobbying for specific legislation (yes, there are shades of gray here, but be reasonable. The Sierra Club does some lobbying but is probably fine. MoveOn does some charity work but we both know it isn't.)
Talking about specific legislation or candidates from the pulpit.
Forming a group so that the Unitarians can work on an political issue that dozens of other groups are already working on, almost always more effectively.
Spiritual Activities -These are fine
Preaching about general principles (taking care of the poor, the sanctity of freedom) without mentioning specific legislation or specific candidates.
Raising money to help people in need (or food, medicine, clothing, school supplies, it’s all fine.)
Building habitat homes
Educating people about what they can do to protect the environment and cleaning up a stream yourself.
Forming a group so the Unitarians can take care of some people in need who aren't being taken care of.
Recall Joel's story about how while the hippies protested that the government should clean up a certain stream, his ROTC guys went and cleaned up the stream.
Don't be the hippies in that story. Be the ROTC guys.