This reminds me of the so-called Bible codes. You know the ones...
Ah, yes, all-too-well.
The problem is not the use (or I should say the overuse and abuse) of logic, but the fact that their basic tenet and unalterable static constant is "no religion is true - there is no God therefore all religion is mere myth and legend."
Yes, I agree that logic in-and-of-itself is not the issue/problem... but rather treating logic as the ultimate criterion of all things. There's nothing wrong with logic, it is a God-given gift that is an inseparable part of our being. You are quite right: the problem with contemporary culture is that instead of keeping logic in submission to the Holy Spirit, logic is rather treated as the "ultimate god" (which, as you stated, actually translates as: "there is no God therefore all religion is mere myth and legend").
The more I study ancient paganism the more contemporary culture looks all-the-more fallen.
As I said before:
"at least the pagans of antiquity knew enough to worship something beyond themselves."
Today, the masses blatantly worship selfish desire, materialism, (fallen) human rationale... and yet the term "worship" is becoming a taboo 4-letter-word.
Lord have mercy on us in these perilous times.