A) were key factors in the increasing proportion of women who died from heart disease beginning in the 1950’s, and warn that
'American Heart Association ... warns', that not 'warn that'
B) that are the key factors in the increasing proportion of women who died from heart disease beginning in the 1950’s, and warn that
relative pronoun 'that' is not needed, etc.
C) were key factors in the increasing proportion of women who died from heart disease beginning in the 1950’s, and warns that
OK
D) that is the key factor in the increasing proportion of women who died from heart disease beginning in the 1950’s, and warns that
relative pronoun 'that' is not needed, etc
E) was a key factor in the increasing proportion of women who died from heart disease beginning in the 1950’s, and warns that
Although 'along with ...' has to be ignored, the subject is 'foods' and verb was does not agree with it