With the law of consecration, there's a clear, but voluntary state, and the end goal isn't the dissolution of the state, but the ending of the expectation to give up your property (the law would go away, but you'd continue to give because you want to). It's not socialism because it doesn't matter who owns the means of production, it only matters that the production is given to the church to be redistributed. It isn't communism because there is a clear state, but I suppose it's close since ideally there wouldn't be any social classes or coercion.
The main similarity is the ideal of "from each according to his ability, to each according to his need", but I think there are enough differences to make it reasonable to say it's not communism, but it is a collectivist system with similar goals.
And I don't really consider it voluntary if I am to believe the consequences that they teach: the threat of being ripped from and permanently separated from your family for eternity is just as coercive of a punishment as the threat of being sent to a gulag.
That is because it is, 100%. If your teacher freaked out over it, she is having trouble reconciling it with the American cultural meme of "Communism is pure evil.", which stems from the Cold War, not religious doctrine.
And yes, something is off if a tithing LDS family is living on food stamps. I have had family who lost jobs and had no money, and the LDS church gave them food and money to cover bills, until they could get back on their feet. Such situations tend to be handled at the local level, and there are definitely good and bad leaders in all organizations, including churches.