Although they are crucially important, a person's total calorie intake is only one of the many factors that determine if their weight will increase or decrease.
Prethinking - Find out the antecedent (SVA) and Conciseness.
Antecedent is Total Calorie Intake, A person's - adjective modifying TCI, hence Subject is singular.
(A)
they are crucially important, a person's total calorie intake is only one of the many factors that determine if their weight will increase or decrease -
(B)
it is crucially important, a person's total calorie intake
is only one of the many factors that determine whether his or her weight will increase or decrease - Correct and Concise.
(C) it is a
crucially important factor, a person's total calorie intake is the
only one of many that determines whether his or her weight will increase or decrease - Many lacks noun.
(D)
crucially important, a person's total calorie intake is only one of the many factors that determines the increase or decrease in their weight. - Lack of antecedent in subordinate clause.
(E) it is crucially important, a person's total calorie intake is the only one of many factors that determines
the increase or decrease in his or her weight - Redundant.