Music should match the occasion and the 4th July is one that has a certain amount of pomp and circumstance. Tchaikovsky's music has a certain power and a certain amount of pomp and circumstance associated with it; as such, it is perfect for celebrating the 4th July and American Independence.
If someone wants to play music from Tchaikovsky's "1812 Overture", there is no reason not to let them. I have no desire to do it, but I also understand that I have no right to impede anyone from doing so, provided they don't overstep their boundaries or cause a disturbance when playing that music.
Great music transcends the boundaries of nationality and era. Although it was written to commemorate the defense of Russia, and contains among its motifs the Marseillaise and God Save the Tsar, Tchaikovsky's 1812 Overture expresses the yearning and fight for freedom and the love of all free people for their countries.
Music such as Tchaikovsky's 1812 overture should be excluded from Events celebrating July 4th. This was written to celebrate Russia's defense against Napoleon, a far cry from our battle of independence from Britain. In addition, although we are a nation of immigrants, in celebrating the birth of our nation, it should largely include music from domestic composers.