The secular Jew is accepted by the religious Jews as one of them, because according to the religion you can't quit Judiasm. Once charged by Jehovah, by birthright, you can't weasel out of it. You have a duty, and maybe you are failing in your duty, but you are still charged with it and so you are still a Jew.

From the secular Jew's perspective, however, there is no god, this duty thing is nonsense... but they feel an affinity to this community because they grew up in it, and because all their friends and family are Jews, and because these Jews still accept them unconditionally no matter what they do. It's hard to walk away from unconditional acceptance. So even though they don't believe in it, they stand by that community as their community, and they try to redefine what a Jew is, wishing to consider it just a race, or even making a national Identity in hopes that this resolves the conundrum. All the while the religious Jew just thinks they are confusing themselves.

Fundamentally this is something they will never agree on. But they can work together for their common good of Jews everywhere despite this.

I could be wrong, but this is my understanding.