Dought & clear, - Is it obligatory to obey a ruler who does not rule according to theBook of Allaah and the Sunnah of His Messenger(blessings and peace of Allaah be upon him)?.

Is it obligatory to obey a ruler who does not rule according to the
Book ofAllaah and the Sunnah ofHis Messenger (blessings and peace of
Allaah be upon him)?.
Praise be to Allaah.
The ruler who does not rule according to the Book of Allaah and the
Sunnah of His Messengershould be obeyed in matters that do not involve
disobedience towards Allaah and His Messenger, and it is not
obligatory to fight him because of that; rather itis not permissible
to do so unless he reaches the level of kufr, in which case it becomes
obligatory to oppose him and he has no right to be obeyed by the
Muslims.
Ruling according to anything other than thatwhich is in the Book of
Allaah and the Sunnah ofHis Messenger reaches the level of kufr when
two conditions are met:
1. When he knows the ruling of Allaah and His Messenger; if he is
unaware of it, then he does not commit kufr by going against it.
2. When what makes him rule by something other than that which
Allaah has revealed is the belief that it is a ruling that is not
suitable for our time andthat something else is more suitable than it
and more beneficial for people.
If these two conditions are met, then ruling by something other than
that which Allaah has revealed constitutes kufrwhich puts a person
beyond the pale of Islam, because Allaah says (interpretation of the
meaning): "And whosoever does not judge by what Allaah hasrevealed,
such are the Kaafiroon (i.e. disbelievers)" [al-Maa'idah 5:44]. The
authority of the ruler becomes invalid and he has no right to be
obeyed by the people; it becomes obligatory to fight him and remove
him from power.
But if he rules by something other than that which Allaah has revealed
whilst believing that ruling by that – i.e. that which Allaah has
revealed -- is what is obligatory, and that it is more suitable for
the people, but he goes against it because of some whims and desires
on his part or because he wants to wrong the people underhis rule,
then he is not a kaafir; rather he is a faasiq (evildoer) or a zaalim
(wrongdoer). His authority remains, and obeying him in matters that do
not involve disobedience to Allaah and His Messenger is obligatory,
and it is not permissible to fight him or remove him from power by
force or to rebel against him, because the Prophet (blessings and
peace of Allaah be upon him) forbade rebelling against rulers unless
we see blatant kufr for which we have proof from Allaah. End quote.
Majmoo' Fataawa Ibn 'Uthaymeen (2/118)