No, properly understood believing in God is not irrational or subjective at all. On the contrary, off-handed dismissal of Christianity is an irrational and subjective decision.
According to the Concise Oxford English Dictionary, 9th Edition:
"Rational" means "of or based on reasoning or reason" and "reason" means "a motive, cause, or justification" or "the intellectual faculty by which conclusion are drawn from premises"
"Objective" means "dealing with outward things or exhibiting facts uncoloured by feelings or opinions; not subjective"
Thus, to be rational and objective a person needs to be impartial and need to ground the decision on something. This means that the person need to think or consider all the evidence, and that this need to be done from a neutral perspective.
In other words, to be fair a balance evaluation of the views of both camps is called for. Judging the veracity of one side through the tinted lens of the other side is akin to making an "objective" analysis with only a superficial understanding of the dynamic of one side and an in-depth knowledge in relation to the other. The bias is clear. This is a trapped that I have fallen into in the past; and sadly, many people still do.
To be objective all the evidence needs to be weighted. This cannot be done in a vacuum, nor can this be done with any preconceived notions. The evidence needs to be put into their proper context. They can only be understood and evaluated properly this way.
Of course, there can be no end in examining the evidence. One can conceivably attempt to find and analyze all the primary text, including going to the original Arabic or Hebrew text and translate it yourself. Yes this can be done if you are that kin.
However, this may not be necessary. Comparison of secondary materials, or commentaries written by other learned authors are often sufficient. After all, even in academic study we do not often study the primary source in every subject that we do. To do so for every subject would take far longer than most people would like to spend in university. Indeed, it may even take a good part, if not the person’s entire life in doing so. Except for the really serious academics among us this is not a course everyone likes to pursue.
Yet despite this non-exhaustive study we do accept the subject matter being taught. And we can and do make judgment in the essay or thesis that we wrote without looking into all the primary text.
On a more general level, when people make a judgment in life they do not usually chase down every single evidence or track down the sources of all statements first. Otherwise judgment would take forever to make, if not impossible.
The point is that we do form judgment on the basis of secondary materials or hearsay evidence in other things we do, whether in academic study or life in general. Provided that we are systematic, non-bias, and maintain an opened mind, such a judgment can be a very sound one. It does not make it any less objective.
This is not saying that we should rush into judgment. Take as much time as you would like, and look into the matters as deep as you wish, but like everything else in life it is very difficult, and is often unnecessary, to be exhaustive. Sooner or later a point will be reached where you will know there are sufficient evidence to tip the scale towards one particular side.
A final point to keep in mind is that there is a limit to what we, human, can know . Not only can we not exhaustively review all the evidence and arguments that bear on your investigation of Christianity (be it evidence to do with reliability, science or other dimensions of concern to you). We also is not capable of knowing things beyond our physical universe. God, by definition and whether you think he exist or not, transcend this universe.
Investigation and rational analysis can only take you so far. It comes a time when you know, or feel, that something is true or not. Once this happens, you can still choose not to agree with your conclusion. There is nothing rational about this end process. It is a very subjective choice. To me a certain amount of "faith" is required to cross the final gap.
