The actor shared his privacy demand in his wife's new Amazon Prime documentary -- "The Greatest Love Story Never Told" ... which puts their whole relationship under a microscope -- which is why his confession is ironic. Ben initially wanted J Lo to keep their rekindled romance under wraps.

He explains, "Getting back together, I said, 'Listen, one of the things I don’t want is a relationship on social media.'" However, he then realized he wasn't being fair -- noting Jen heavily uses social media and has hundreds of millions followers.

Once he considered this, Ben says he caved -- adding ... "It’s sort of like, you’re gonna marry a boat captain and you go, 'Well, I don't like the water.'" BA finished by saying ... "We're just two people with different kinds of approaches trying to learn to compromise."

Of course ... Bennifer first got together in 2002 -- but called things off for good by 2004 ... or, so we thought at the time. They got back together almost 20 years later and started again.

TMZ broke the story ... the former flames rekindled their love story in 2021 -- getting married that next year in a lavish ceremony in Georgia. Since then, they've been inseparable.

While Ben says he's relented on the no-social-media stance -- it appears Jenny has at least somewhat respected his original wishes ... as he only pops up occasionally on her social media accounts.

In fact ... Jennifer confirmed in her doc that her husband isn't really a fan of the spotlight -- but called him her muse for her ninth studio album, "This Is Me...Now." So, he was front and center for this project -- whether he liked it or not, and he seems to be cool with it.

Ben may've been a reluctant participant ... but he certainly assisted in bringing to life the final product -- as it was his idea to capture every single behind-the-scenes moment.