Let's be clear here: Catholics do not take this stance - faith MUST be supported by reason. The Catholic position:
Catechism Paragraph 155: In faith, the human intellect and will cooperate with divine grace: "Believing is an act of the intellect assenting to the divine truth by command of the will moved by God through grace."
In more depth:
Catechism Paragraph 159: Faith and science: "Though faith is above reason, there can never be any real discrepancy between faith and reason. Since the same God who reveals mysteries and infuses faith has bestowed the light of reason on the human mind, God cannot deny himself, nor can truth ever contradict truth."37 "Consequently, methodical research in all branches of knowledge, provided it is carried out in a truly scientific manner and does not override moral laws, can never conflict with the faith, because the things of the world and the things of faith derive from the same God. The humble and persevering investigator of the secrets of nature is being led, as it were, by the hand of God in spite of himself, for it is God, the conserver of all things, who made them what they are."
And finally, and perhaps most significantly:
Catechism Paragraph 50: By natural reason man can know God with certainty, on the basis of his works.
By this is it meant that through philosophical reflection God's existence can be known.
You can argue that philosophical reflection will reveal something different (ie, that he cannot be known), but you can't assert that Catholic religious belief involves belief in something without evidence. This is completely false.