First, it's not a pledge to the President, it's
"to the flag of the United States of America, and to the Republic for which it stands".
And yes, I say the pledge, the non-religious (1923) version.
Generally it's once a month, at the opening of a meeting.
loyalty to a person, country, group, etc.
the fidelity owed by a ... citizen to a ... government
devotion or loyalty to a person, group, or cause
I see no conflict between loyalty to one's country and to one's imaginary friend.
In fact, many people here make a big deal over their loyalty to the USA, protect the Constitution at all costs, etc.