Question: "Should an Orthodox Christian make donations to the Salvation Army?"
You could certainly do a lot worse with your money than to give to the Salvation Army.
Many are unaware that the Salvation Army is actually a Protestant denomination, rather than just a charitable entity. It was founded in 1865 by William and Catherine Booth. It is part of the Wesleyan / Methodist tradition, and is theologically almost identical in belief to other Holiness denominations, such as the Nazarene Church that I grew up in. It is different from just about every other Christian group when it comes to the Sacraments. Salvationists reject all Sacraments, including baptism and the Eucharist. As their name suggests, they are structured a military model -- with clergy have the ranks of officers, and laity being the enlisted. When you join the Salvation Army, you sign the Articles of War, rather than receive baptism. Their churches are called "citadels" Another interesting feature of the Salvation Army is that married officers are required to have the same "rank" as their spouses. This is in large part due to the high level of commitment that they require of their officers, but also due to their belief that this work requires a team effort on the part of such a couple. The charitable work of the Salvation Army is impressive and admirable. I think that it would be a good idea for the Orthodox Church to encourage people to emulate much of what they do.
But to answer the question, some would argue that because they are a Protestant denomination, we should not give to them because in some traditionally Orthodox regions they have attempted to convert people to their faith. A case could also be made that since Orthodox Christians in America are a small minority, and our own charitable organizations attract a lot less general support, we should support our own charitable works and let the Protestants support the Salvation Army. On the other hand, there are things that the Salvation Army does that no Orthodox charity that I am aware of is currently doing -- for example, I know that in Houston they run a family shelter that tries to help homeless families without splitting them up. So personally, I think if you are donating to some specific purpose like that, there is nothing wrong with that.
My own mother was born in a Salvation Army hospital, and so I am glad that despite their theological shortcomings, they have in practice been such good examples to the rest of us.