For the true thinker the deconstruction of reality by questioning accepted institutions and relativism towards reality is only the first step of attaining knowledge. The reconstruction of reality by understanding the phenomenon that exist and their analysis leads to full knowledge.
I think that Decartes did not give up religion because, back then, it was an accepted rule that everything is questionable but the rule of the Christian Church was unquestionable. The mediaeval age and the Renaissance were abundant in magnificient discoveries in law and philosophy (the interpreters' revolution -read Pierre Legendre) but their point of reference was different from ours. (vide the text from Athanasius in Italics)
The question whether Christianity is compatible with philosophy exists in all religions.
Philosophy is useful in explaining the tenants of the Faith, but in the hands of the Church it is but an instrument of accomplishing the implementation of the Kingdom of God by seducing human thought toward the lust of things unspeakable, invisible and utmostedly divine.
Something I'd like to comment on is the use of the word "logic" towards the Christian religion. The word logic is rooted in the Greek LOGOS.
The rules of scholastic logic attain a value of null within reference to the Divine. Philosophy has this problem that it interprets logos as an assortment of sounds/symbols, something we produce. The Theo-logos is not just a symbol but it is a reality born of the Father, once in eternity and once incarnate. The logos, the logic of philosophy is lifeless and formalistic. The logic, the logos of God is alive and material in being. To attain salvation we must reject the rationality of common sense and accept the so-called irrational, the logic of the Logos. With the questioning of human existence in its current state, we deconstruct reality, we destroy rationality to accept the true ratio of being. The ascetical quest for the re-creation of the primordial intelligence, which classical philosophy has maintained is the ideal is misguided. The quest for primordial consciousness of the cave vide Plato, shows the dirty face of factually true knowledge. One has to go beyond logic and small l logos to understand the logic of the city of man.
I suggest reading Athanasius's Oratio contra gentes 40
Athanasius Against the Heathens 40
40. The rationality and order of the Universe proves that it is the work of the Reason or Word of God.
Who then might this Maker be? For this is a point most necessary to make plain, lest, from ignorance with regard to him, a man should suppose the wrong maker, and fall once more into the same old godless error, but I think no one is really in doubt about it. For if our argument has proved that the gods of the poets are no gods, and has convicted of error those that deify creation, and in general has shown that the idolatry of the heathen is godlessness and impiety, it strictly follows from the elimination of these that the true religion is with us, and that the God we worship and preach is the only true One, Who is Lord of Creation and Maker of all existence.
2. Who then is this, save the Father of Christ, most holy and above all created existence , Who like an excellent pilot, by His own Wisdom and His own Word, our Lord and Saviour Christ, steers and preserves and orders all things, and does as seems to Him best? But that is best which has been done, and which we see taking place, since that is what He wills; and this a man can hardly refuse to believe. 3. For if the movement of creation were irrational, and the universe were borne along without plan, a man might fairly disbelieve what we say. But if it subsist in reason and wisdom and skill, and is perfectly ordered throughout, it follows that He that is over it and has ordered it is none other than the [reason or] Word of God. 4. But by Word I mean, not that which is involved and inherent in all things created, which some are wont to call the seminal principle, which is without soul and has no power of reason or thought, but only works by external art, according to the skill of him that applies it—nor such a word as belongs to rational beings and which consists of syllables, and has the air as its vehicle of expression—but I mean the living and powerful Word of the good God, the God of the Universe, the very Word which is God John 1:1, Who while different from things that are made, and from all Creation, is the One own Word of the good Father, Who by His own providence ordered and illumines this Universe.
5. For being the good Word of the Good Father He produced the order of all things, combining one with another things contrary, and reducing them to one harmonious order
. He being the Power of God and Wisdom of God causes the heaven to revolve, and has suspended the earth, and made it fast, though resting upon nothing, by His own nod. Illumined by Him, the sun gives light to the world, and the moon has her measured period of shining. By reason of Him the water is suspended in the clouds; the rains shower upon the earth, and the sea is kept within bounds, while the earth bears grasses and is clothed with all manner of plants. 6. And if a man were incredulously to ask, as regards what we are saying, if there be a Word of God at all , such an one would indeed be mad to doubt concerning the Word of God, but yet demonstration is possible from what is seen, because all things subsist by the Word and Wisdom of God, nor would any created thing have had a fixed existence had it not been made by reason, and that reason the Word of God, as we have said.