Can an innocent son of a man convicted of treason be eligible to hold an office of honor or trust in the US?

Answer 1

Certainly. Corruption of Blood and forfeiture were excluded in the US Constitution. Holding the sins of the fathers against the sons "...until the third and fourth generations because their teeth have been set on edge by sour grapes" was done away with not because of the United States' Judeo-Christian heritage, but because the Colonies had been so battered by the British Crown and its seizure of property from those whom it considered disloyal. The prohibition against such was incorporated into the US Constitution. Art.1, Sec. 9, cl. 3. The US Constitution did away with the notion of punishment beyond the evil doer, long before the Bill of Rights.

(Corruption of the blood means that your parent committed a crime against the State, and that generations were effectively held responsible by the loss of the right to inherit; forfeiture meant that existing property was seized by the State.)

Forfeiture and Corruption of Blood were some of the particularly offensive ways that the then British Crown punished the original American colonists. As a matter of fact, all colonists, everywhere. The American Colonists objected strenuously.

While you are not supposed to be discriminated against under law or absent special circumstances, be subjected to forfeiture, your passing a security clearance or being voted into a public office, or being appointed to a high position of trust or honor is another matter. While not a processes of the judiciary, your history could cause difficulties, depending on the nature of the office, not in the legal sense, but in the practical world.