My experience is different.
First off the whole idea of non-religious Jews is strange, when you think about it. You don't hear terms like "non-religious Methodists" very often.
That's because if you stop believing in Methodism you are simply not a Methodist at all.
But because Judaism is both a religion and a closely tied ethnicity this term when applied to Jews is common.
But a lot of Jews who perhaps don't believe in God, or believe in God very weakly still feel that Jewish tradition is important and will celebrate Passover and perhaps other Jewish holidays. So, in my experience (with friends) a lof of so-called "non-religious Jews" still have a lot more connection to their religion than, say, someone who was raised Catholic but who has become an atheist.
The net-net is there are not a lot of truly "non-religious" Jews. The three main denominations sort of align with this: Orthodox have a traditional view of the religion, while the Reform Jews might only be as religious as Unitarians (which is to say agnostic), but are still part of a religious tradition.
I would suspect that only a very small percent of American Jews (say under 20) were raised outside of any Jewish religion, and yes, some of them may have been committed Communists. But I would be surprised if that was ever even 5% of Jews in the USA.
So, it doesn't really explain the 70% of Jews who routinely vote Democratic, or why most Jews embrace so many liberal social causes.
The thoughtful Jewish writer Norman Podhoretz wrote a book "Why Are Jews Liberals?", which I read a few years ago. One of the answers isn't "because they were raised as atheist commies". Speaking of broad groups, there are, of course, a few individuals who will exactly fit that description. (Micheal Savage calls them "red diaper doper babies", and seems to know who they are.)
