I’ve never liked the word “lifestyle” when it’s applied to being childfree. It has a lot of derogatory feeling to it. The word “lifestyle” has the connotation of doing something not only uncommon but also somehow deviant. A lifestyle is something that other, abnormal people have, whereas the good, healthy, normal people just live their lives. “Childfree lifestyle” sounds like we’re all swingers or we are sunk in mindless decadence. (Some of the childfree no doubt are, but not in any greater percentage than any other population cohort.)
People refer to Hugh Hefner as living a “lifestyle.” We would never say that Mother Teresa had a “lifestyle,” though she clearly lived life according to a very unusual plan.
People who are hostile to homosexuality are generally the ones who call being gay a “lifestyle.” We generally don’t refer to a social conservative as someone living a lifestyle, nor do we refer to a “straight lifestyle" or "heterosexual lifestyle."
By the same token, I’ve never heard anyone refer to a “parenting lifestyle” or a “childed lifestyle.” Saying I live a "childfree lifestyle" is to suggest a lesser way of living than a life with children.
My preference would be to make it shorter. Save a few keystrokes. Why not just “childfree life”?