Are they still entitled to U.S. citizenship?
While American citizenship law is generally quite straightforward compared to that of other nations, the status of Lafayette and his descendants a is particularly interesting question.
At the time of the independence of the United States in 1783, any white person resident within the borders of the states and its dependent territories was considered to be a United States citizen. The status of loyalists was a grey area that sometimes varied by person to person. Some loyalists who were determined to stay in America were required to take an oath of loyalty to the United States government while others, such as Lord Fairfax, were essentially left to their own devices due to age and a general sense of respect for their contributions to colonial society. At any rate, virtually all loyalists saw at least some of their land confiscated, which caused as many as 100,000 of them to "evacuate" to Britain, Canada and the West Indies.
Congress established the general principles for citizenship after the passage of the Naturalization Act of 1790. This held that anyone born on American soil would automatically become a United States citizen, that new immigrants would have to live in the United States as a resident for a certain amount of time before applying for citizenship, that children born overseas to American fathers were full-fledged American citizens and that an oath of allegiance was required of all new applicants for naturalization. This didn't address the issue of naturalization by the states of the nascent republic. In 1784, Maryland passed "An Act to naturalize major-general the marquis de la Fayette and his heirs male for ever", which at the time legally made Lafayette an American citizen in the eyes of the Federal Government. However, in Dred Scott v. Sandford (1857), the Supreme Court ruled that while states could effectively grant whatever citizenship they liked, being a citizen of a single state did not confer federal citizenship with all of the rights and duties that entailed. Citizenship of a state is therefore a form of honorary citizenship while "real" citizenship, in a political sense, has been the exclusive domain of the Federal Government since the passage of the Constitution of the United States in 1789.
There were two test-cases regarding descent from the Marquis de Lafayette in the 20th century. The first attempt was filed by Count René de Chambrun on the eve of the Second World War. Chambrun had all of the right American credentials: a French aristocrat and matrilineal descendant of Lafayette, he was also the nephew of Alice Roosevelt and the son of an American mother. Unfortunately for Chambrun, his father-in-law was a French fascist and his godfather was Philippe Pétain. While the New York State Court of Appeals accepted Chambrun's claims for citizenship for the purposes of taking the New York State Bar Examination, the State Department declared that Chambrun was not a United States citizen in 1936.
A similar incident occurred in 1955, when Count Edward Perrone di San Martino attempted to claim United States citizenship based on the Maryland resolution. At that time, the State Department definitively resolved that any grant of citizenship to the descendants of the Marquis de Lafayette were honorary while leaving open the question as to whether or not Lafayette himself was an American citizen ad-personam. According to the Naturalization Act of 1790 and its succeeding acts, the grandchildren of Lafayette were ineligible for citizenship as none of their fathers had ever been an official resident of the United States, thereby making the question doubly-moot.
It is interesting to note that descent from a specific person isn't an issue unique to the United States. British citizenship law allows that any descendant of the Electress Sophia is entitled to British subject status -- effectively allowing any descendant to carry a British overseas passport but without the right of abode. This was established in the Sophia Naturalization Act 1705 (4 & 5 Anne c. 16) and continues to remain in force by right of the British Nationality Act 1948 (11 & 12 Geo. 6 c. 56) which recognizes the right to either British citizenship or British overseas (colonial) citizenship to the heirs of the body of the Electress Sophia.
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