In my own understanding, there are some central dogmas such as the Trinity, the Incarnation and Divinity of Jesus, and others which are so central to Christian faith you can’t be a Christian without them. The main dogma I can think of in this case is that God is a Trinity; many of the worst heresies in Christian history came from those who denied God was triune, or that Jesus was not divine.
There are also some doctrines, such as Papal Infallibility, and others. A Catholic in my view is bound to believe absolutely in things like the Holy Trinity, the Incarnation of Jesus, and the material stated in the Nicene Creed. A Catholic in my view can question other doctrines or examine them more deeply to try and understand why the Church teaches them, if he feels they may be wrong. Faith in my view is not blind obedience and a suspension of one’s faculty of reason, as St Thomas says, God is Truth and cannot err, so whatever is true anywhere must come from God. If one feels something is false, then by conscience one should carefully examine the arguments and views and only judge it to be in error if it agrees with reason and with conscience.
For example, if a future Pope were to declare all Muslims were pagans and Catholics were bound, on pain of excommunication, to go on a Crusade against Muslims, and used his infallibility to endorse this belief, I would consider it acceptable to reject it even if I had to leave the Church, as such a pronouncement seems brutally against the sensible teaching of the Church as it is now as well as what scripture itself says about love and forgiveness. Or, if one for example believed the Inquisition and its torture of suspects was a grave evil and the Church was wrong to do it (as I very firmly do) in the past, I don’t believe this is grave sin. I also believe the condemnation of Galileo was a grave error and Pope John Paul the II himself admitted this.
However, it is another thing to disagree with some foundational teaching of the church, such as the grave immorality of murder and abortion. The Church’s magesterium, many Popes, and also many Saints and great Doctors of the Church have always through the ages regarded both unjustified homicide and abortion as grave evils. Even if abortion is held to be a grave evil by the church is not a binding dogma like the Holy Trinity, I don’t think Catholics should disobey or teach against this without very grave or good reasons. And if they do so, they should leave the Church. I would, if I could not accept a core part of the Church’s teaching.
A Catholic in my view can privately hope for reform in some areas, such as the role of the women in the ordained priesthood. But a Catholic should pray and wait patiently for reform to come to the Church. Vatican I and II for example brought many great reforms to the Church with no-one probably would have thought possible, and the Church is not a monolithic institution with no life or ability to adapt; it is much more a unity in great diversity, even in matters of theology and spirituality. But it is one thing to privately desire the Church reform in one way and publically denounce the Church or one of its teachings without good reason, and to bring scandal upon the Church does great damage to both it and the faith as a whole, which is why any Catholic needs to take these matters with great care and only dispute a teaching of the church only after considerable maturity, reflection, and with a clear and well informed conscience and mind which is familiar with the church and its heritage at a deep level.
In my experience Catholics are actually very flexible and open when it comes to theology, and are not afraid of having a good and open discussion. The Church must teach very firmly on some things in light of the widespread relativism which exists today, but at the same time there is a lot of beautiful variety in the Church, it’s teaching, its philosophy and theology, and its various traditions.