Natural reason is not able to save us. Explaining why the Mosaic Law was given to Israel, St. Thomas writes:
It was most fitting for the Law to be given at the time of Moses. The reason for this may be taken from two things in respect of which every law is imposed on two kinds of men. Because it is imposed on some men who are hard-hearted and proud, whom the law restrains and tames: and it is imposed on good men, who, through being instructed by the law, are helped to fulfil what they desire to do. Hence it was fitting that the Law should be given at such a time as would be appropriate for the overcoming of man's pride. For man was proud of two things, viz. of knowledge and of power. He was proud of his knowledge, as though his natural reason could suffice him for salvation: and accordingly, in order that his pride might be overcome in this matter, man was left to the guidance of his reason without the help of a written law: and man was able to learn from experience that his reason was deficient, since about the time of Abraham man had fallen headlong into idolatry and the most shameful vices. Wherefore, after those times, it was necessary for a written law to be given as a remedy for human ignorance: because "by the Law is the knowledge of sin" (Romans 3:20). But, after man had been instructed by the Law, his pride was convinced of his weakness, through his being unable to fulfil what he knew. Hence, as the Apostle concludes (Romans 8:3-4), "what the Law could not do in that it was weak through the flesh, God sent [Vulgate: 'sending'] His own Son . . . that the justification of the Law might be fulfilled in us." [ST I-II, Q98, A6; ellipsis in original; emphasis added]The Catholic Faith is not Gnostic, as though we are saved by knowledge, and we cannot reason our way to salvation.
In point of fact, we do not believe that our salvation is contingent upon "getting it right" in terms of things we explicitly believe or think. Objectively and formally the Catholic must believe that which the Church teaches; subjectively and materially there may be various obstructions impeding one's belief in those things. The mentally handicapped may not be able to believe in any of the dogmas of the Church, but this does not mean that he is unable to be saved. Some dogmas may be entirely beyond another man's ability to understand, but this does not mean he is doomed to hell. As we have seen in this series, we are saved by Christ and not by anything that we do or think, and so ignorance of the truth likewise does not condemn a man.
It seems that many Protestants do not think through this problem, probably because it's not at all typical among them to think about the importance of the difference between formal and material apprehension of the truth. They say that we are saved "sola fide," but on their telling of the tale one must wonder then how (for example) the mentally handicapped can be saved who are unable to exercise such a faith. Perhaps some will make allowances for that inability (which is good), but one then wonders how they can consistently say that other sorts of real impediments to "sola fide" are irrelevant, and that those prevented by those obstructions from exercising it are nevertheless doomed to hell. There is also, in some respects, a Gnostic element to Protestantism: it's not just that one is saved by faith alone, but that he must also believe that he is saved by faith alone. But does not this fly in the face of the related belief held by Protestants that man is saved by Christ alone? Is it not contradictory to say that salvation "by Christ alone" includes the requirement that you must explicitly believe you are saved by "sola fide"? It seems to me that it does.
But the Catholic Gospel is not like this. We are not saved by what we know, and those who are genuinely unable to believe dogmas of the Church are not by that defect condemned. We are saved by grace alone; we are saved by Christ alone. Our reason cannot save us.