Perhaps you might explain ...
Galatians 6
King James Version
1 Brethren, if a man be overtaken in a fault, ye which are spiritual, restore such an one in the spirit of meekness; considering thyself, lest thou also be tempted.
Clearly a brother is in view. We do not seek to restore unbelievers. Secondly, the same thing can occur to those who are haughty towards one overtaken in a fault.
2 Thessalonians 3:6
Now we command you, brethren, in the name of our Lord Jesus Christ, that ye withdraw
yourselves from every
brother that walketh disorderly, and not after the tradition which he received of us.
I think it reasonable to suggest that you are not considering that our Faith and our faith have two differing aspects: Godward, and Manward; eternal, and temporal. Just because we have faith in Christ does not mean we cannot be weak in faith.
Romans 14:1-3
King James Version
1 Him that is weak in the faith receive ye, but not to doubtful disputations.
2 For one believeth that he may eat all things: another, who is weak, eateth herbs.
3 Let not him that eateth despise him that eateth not; and let not him which eateth not judge him that eateth: for God hath received him.
That weakness in faith could succumb to anger is not unreasonable, either.
I would suggest to you, that, in denying the potential for a believer to fall into sin such as expressing unbelief is an extreme position forced by your own views. It also suggests a view that we are saved by faith through grace.
Of course the Lord keeps us, He is the Finisher (Perfecter) of our faith, not just the Author. In the process of life, all believers will go through growth and vary in strength concerning the manward aspect of their faith. I say all of this for this purpose: that you be careful not to sit in judgment of others who may very well be born again believers in the throes of rebellion. As with any you "believe" to be unbelievers, the goal is to speak the Words of Life, not the words of judgment. Because you have no power to to convince of sin, righteousness, and judgment that leads to salvation.
The reality is that even born again believers can fall into sin, and there is nothing in Scripture that makes it clear they cannot get to a point of anger towards God that they deny Him. I don't think this is something that is common, but I do allow for it.
And what's more, I can understand it, from a manward perspective.
The loss of a child is something I will never have to go through, because I have no children. I can relate in regards to loss of relatives, and even the loss of beloved pets. That a babe in Christ (and let's face it, a majority of believers will spend much of their walk in diapers due to a failure to grow) would get angry with God over the loss of a child (or even a spouse) doesn't change the fact that God will still finish the work He began.
Lastly, our very daily conversation can be equated to a rejection of God. If we reject His will for our lives, do we not deny Him? Are we not all guilty at some point of this sin?
I will give this matter more study, because it is a matter one might place in the grey area column, so I know it'll need further support.
God bless.