He was duly elected in accordance with Tradition. Holding fast to Tradition requires accepting that he is pope. It doesn't preclude us from believing that he's a bad pope.
It's not within the province of the the laity to declare a pope invalid.
On core doctrine he is exactly like all Popes before him.
Liberals will soon realize this and jump on him like a bull dog on a porkchop.
Besides, you have not answered the question of whether Francis professes the Catholic Faith. I think it's because there is much doubt as to whether he in fact professes the one true faith.:
Actually only those are to be included as members of the Church who have been baptized and profess the true faith...
- Pope Pius XII, Mystici Corporis Christi, 1943
"You are not to be looked upon as holding the true Catholic faith if you do not teach that the faith of Rome is to be held"
- Pope Leo XIII, Satis Cognitum, 1896
Does Francis teach that the faith of Rome is to be held?