What it means is that people will latch onto something, even if it is self contradicting, illogical, irrational, etc.
As history has shown, in a secular society that situation has given rise to the most destructive forces in history.
The simple reason is that most non-God based belief systems ultimately put their faith in man, who then in turn creates their own morality.
Ravi Zacharias once made an astute point that the horrors of the Holocaust were made possible in the lecture halls of German Universities, where the philosophies of the time squashed religion and elevated the self. Nietsche’s groundwork for existentialism and postmodernism are prime examples. Hegel’s work that denied the existence of absolutes also played a role. There are other examples as well.
Your problem is that you are lumping anything that isn't Christianity into a single bucket called secular. That's just to big a bucket.
But here is some food for thought:
Hitler wrote the following in Mein Kampf:
"I believe that I am acting in accordance with the will of the Almighty Creator: by defending myself against the Jew, I am fighting for the work of the Lord.."
And here is another:
-Adolf Hitler speech - Berlin 24 Oct. 1933
"We were convinced that the people needs and requires this faith. We have therefore undertaken the fight against the atheistic movement, and that not merely with a few theoretical declarations: we have stamped it out".
So maybe Nazism wasn't quite so secular as you might think.