I don't think anyone can fail to recognise or accept that in general people without children have more money that people with children.
That's the problem with generalisations though - you can't rely on them in specific situations and it's ridiculous to keep harping on - whether it's a poster on here or a rl friend - that that person must be rich due to one element of their lifestyle, without taking into account (a) all other factors or (b) the lived experience that they are telling you about.
Social mobility plays a part in this debate. I am part of a group of friends where I'm not only the only childfree member, but also the only one from a working class background. I have a decent job with a decent wage but DH earns minimum wage and I send significant amounts to family abraod to pay for healthcare. We get by - we are lucky enough to have a nice but quiet standard of living, one holiday per year, occassional treats etc, so long as there's no major household emergency (a couple of years ago, our washing machine, cooker and freezer and died within a week of each other and that was enough to push us onto the bones of our arses). Every single one of my friends in this group, however, have a much higher standard of living than we do - huge houses, multiple holidays, designer clothes, if they want something (for themselves or kids) or they just go and get it. I love these women but they make huge assumptions about my bank balance, because they take their situation and subtract all the costs that go to their kids. When I baulk at the idea of an impromptu weekend in New York, or catching up over dinner in a michelin star restaurant, I am told that I surely must be able to afford it due to having no kids.
I am able to recognise that these friends are outside the parenting norm and wouldn't say that all parents are loaded and better off than me because that is my immediate experience. It seems that recognition tends to go one way though.
Money is such a personal and emotive topic though. It's horrible to have to keep explaining and justifying your lack of it to those who don't get it and that applies to parents, non-parents, couples and single people depending on individual circumstances.