I suggest that Mr. Shapiro is wrong.
Oh, he's correct, that most Jews are secular, and not religious. And that many Jews are atheists* (like me, for instance).
But that's not why Jews vote Progressive (not "Democrat"; but Progressive).
A very important part of the Jewish world view and life view is a concept that, in (transliterated) Hebrew, is called Tikka Olam.
Tikka Olam, in English, means "to fix the world."
Jews see their social and religious missions as callings to "fix the world." Jews want to make the world "a better place."
Note that no Jew can tell you whether it is necessary that the "fixed world" suit you — or them for that matter. Nobody has defined "better."
All they know is that the world isn't working correctly right now, so it needs to be fixed.
How would "working correctly" be defined? Nobody really knows.
But the Jews do know that the Progressives are also out to "fix the world," and to "make it a better place."
So therefore, if a Jew who has never learned to think critically truly wants to make the world a better place, then that non-critical-thinking Jew votes for Progressives. They, after all, are doing the right thing.
And how does the non-critical-thinking Jew know that the Progressives are doing the right thing? Why, because the Progressives continually tell us so.
So it must be true. Right?
*So, why are so many Jews actually atheists? Ah, that's really easy to answer.
Jews are raised to discuss everything, especially religious matters.
These discussions very often become heated, with yelling. "I'm right! You're wrong!" and stuff like that.
So since Jews are trained to argue about religion, it's an easy step to also argue with God. Indeed, there are many Jewish jokes (by Jews about Jews) which involve arguing angrily directly with God, and how God answers these arguments.
Well, if you've been brought up to argue with God, it's an easy step to seeing God as being wrong. And the very next step is to believe that, because God has not really answered me directly, then God really doesn't exist. QED
The Ultra-Orthodox (Hasids, for instance) solve this problem by joining one or another group, each led by a know-it-all Rabbi whom they venerate almost as if he were God's appointed messenger or judge. The members of a group do whatever their Rabbi tells them is the right thing to do.
Trouble is, each of these venerated Rabbis has his own idea about right, wrong, and how to accomplish Tikka Olam. And none agrees with any other. And their separate groups (call them congregations) are not on speaking terms with one-another, either.
So now you know about Jews.