They can’t be forced to say it: West Virginia State Board of Education v . Barnette, 319 U.S. 624 (1943).
Even so, being born a US citizen implies implicit allegiance to the constitution.
Of course, children cannot commit to explicit anything, contracts, binding agreements etc until they reach the age of majority.
Once achieved, they are by matter of national fabric, expected to have fidelity to their nation.
Of course, since it is implicit, no actual oath or pledge is required, it is a natural law issue.
Those entering into service in the military or public derive are required to affirm or swear loyalty to the US Constitution and no other.
Hence, the requirements of sole US citizenship for those entering into commissioned service or high office.