Words are important, and the suffix "-free" is deeply problematic in regards to this debate. People without children are childless, not childfree. Using the term 'child-free' is goady, exclusionary, inflammatory and offensive.
Other uses of the suffix -free all refer to things that are unwanted, unwelcome or unpleasant. Cancer-free. Rent-free. Smoke-free. Gluten-free. Worry-free. The antonyms of -free include burdened, hindered, encumbered. It is objectionable for anyone to imply that parents' relations with their children should be described in those terms - even if it is couched in 'positive' language intended to make their life choices, or life outcomes, more validating. It's patently obvious that many (not all) of the most vociferous proponents of the right of a subset of Mumsnet posters to a forum where they can exclude the core constituency of the entire site have some major issues in respect of their childless status that they are still working though.
But a successful forum is about posters' behaviours, not their identities. Nobody knows, or need know, whether any individual poster on any given thread has zero, one, two or twenty children, unless they elect to share that information in the context of that thread. Same goes for whether a poster has zero, one, two or twenty dogs, or cars, or verrucae. I can understand why, if the demand is there, people might want to group threads together into a forum that caters for people who have an interest in dogs, or cars, or verrucae, but it would be extremely odd if people petitioned for a special forum to cater exclusively for posters who are dog-free, car-free, or verruca-free - even though there are probably a great many MNetters who are all of these things. It's the attempt to claim the position of being childless as an identity, branded as "free", and the demand that this needs a ringfenced space on a website for parents in which that identity is the dominant one, that is being objected to. Not the number of children someone does or doesn't have.