Well actually, parts of the United States used to be not only the Confederacy but also; Mexico, Spain, France, the Republic of Texas as well as Britain. Therefore, each of these nations and their cultures are equally important to American History.
As for me, with a home in Louisiana and a home in Texas I have no problem whatsoever if my neighbor in Louisiana flies a Confederate Flag or my neighbor in Texas flies a Mexican Flag. Actually, in New Orleans my neighbor is more likely to fly a French Flag.
What is most important is that each flag and nation is respected and that everyone within the borders of the US respects this nation, just as I respect the cultures of other nations when I visit or live overseas.
A private residence is not a public, taxpayer supported government building.
The two cases are very different.