Edward was already looking for an "out" so Mary, a Catholic, couldn't take the throne. He didn't want Elizabeth either but it had nothing to do with whether Elizabeth was Protestant enough or not.
Henry VIII's will named Mary and Elizabeth in the line of succession after Edward. The provision in Henry's will on succession was submitted to Parliament which approved the provision under the name "Act of Succession of 1543". Now Edward did love his half-sisters, though Mary's religion drove him nuts and caused numerous arguments between the two. However, in spite of Henry's will and the Parliament Act, Edward didn't consider either of his 2 sisters eligible to take the throne due to their "questionable" birth status. Henry had his marriage to Catherine of Aragon annulled making Mary "officially" illegitimate. In ending his marriage to Anne Boleyn, Henry had that marriage annulled making Elizabeth "officially" illegitimate. This made both Mary and Elizabeth ineligible for the throne. Henry ignored this and named them anyway.
So Edward was already inclined away from his sisters anyway. However, Edward couldn't go against Henry's will, and more importantly an Act of Parliament, without a strong, acceptable substitute. Northumberland took this inclination, ran with it and convinced Edward, which wasn't that difficult, to go with Jane. Northumberland then convinced Jane's parents to marry Jane to Northumberland's son. Since both Jane and her husband were underage, Northumberland would be made regent and defacto King.