I totally understand why somebody would prefer not to describe themselves as 'childless'. The -less has connotations of something missing, of being somehow inferior or lacking when compared with people with children. It makes 'having children' the default, and 'not having children' abnormal. I get it.
But something about 'childfree' really grates with me. The -free seems to imply liberation from the idea of children, as if that's some obligation or burden, or as if they're something to be escaped from at all costs. Basically, I think it sounds as much like a smug value judgement as 'childless' is a thoughtless one.
Not sure what the alternative would be, but how about 'nonparent'? It needs to be a word that's totally neutral about whether having kids is a good or bad thing.