Mary Gingell of Annandale questioned the role of the federal government in funding museums, libraries, national parks and performing arts centers {letter, Oct. 11}.

She attacked what Americans hold dearest without realizing the consequences. If the preservation of our heritage and environment is not the responsibility of the federal government and every American, whose responsibility is it? If the cost of maintaining the Smithsonian, Library of Congress or the national parks were not shared by all Americans, not all would be able to afford to visit and use them. Whether you earn $10,000 or $10 million, you can see the Grand Canyon, Old Faithful and any of the museums and parks and know that these American treasures belong to you. These monuments and institutions hold in trust the natural and cultural heritage of all Americans.

Mary Gingell is plotting the demise of our national heritage. By supporting parks and cultural institutions we are committed to ensuring that this national wealth will be there for our generation and the next. They are part of our national spirit and life. Mary Gingell says that these institutions should be sold so that government can adhere to its main task of ''protecting the lives, liberty and property of American citizens.'' Isn't that what the Smithsonian, national parks, National Gallery of Art and the Library of Congress are doing? RANDI KORN J. DANIEL ROGERS Alexandria