Are you allowed to doubt if you are a Christian? Well, maybe another question that might be helpful is whether anything is completely doubtless?
In science there is still an element of doubt. Scientists create hypotheses and tests them out, but even so they will admit that experiments only help them guess at conclusions; highly educated guesses mind you, but guesses still the same.
In law there is an element of doubt. The case is presented and when it comes to criminal law the requirement is "beyond reasonable doubt". Not beyond a shadow of doubt. Just reasonable doubt.
But when it comes to faith, somehow we raise the bar to be without any doubt whatsoever. Any questions we have about God, about His character, or His methods and we are ready to give up our faith. I know I've been in such situations personally before.
Part of the problem is that while God makes Himself known, He is also beyond our full comprehension (Is 55:9). Just imagine: God is able to know every thought and action of every single human being in any given moment. What we can process is a drop in an ocean compared to all that God is.
What I've found is that I often forget this. I don't know why, but I often picture God as very much human; knowing that same as us humans, and behaving the same as us too. What happens when doubt enters our mind is that we are unable at that time to comprehend fully why God is doing/allowing/not doing something. This doubt can push us away from God because we can't understand something about God. We often fill in the blanks with thoughts that God isn't good, or doesn't care for me.
That doesn't have to be the way that doubt operates though. I have found that if I see doubt as an invitation to see God clearer, to explore a part of God that I hadn't previously explored before. It's not unlike a real relationship when you think about it! There are times when I don't understand why Bec is doing something. And in those moments I can choose to stay in doubt and become insecure about our relationship. But when I do make the effort to try to understand what is going on in her world it draws us closer together.
The question we end up with is whether we are going to feed our faith, or fuel our doubts. This is a choice each and everyone of us will have to make.