These are not, alas, new sentiments among many UUs. For people who think UU worship (they'd prefer the word "program") is all about thinking and intellectual stimulation, and for ministers who value their words above life itself (I am a minister, so I can say this), the presence of children is an issue. As a member of one congregation I served wrote (complaining to the Board about me and my new custom of inviting the children to be part of the first 20 minutes of the service) and this is a direct verbatim quote: "I come to church for intellectual stimulation with my peers, and children are not my peers." So there.
There probably is room for a club without children, even a UU club, though you couldn't call it any more than a club, and I strongly doubt their buildings would be beautiful enough to wind up memorials to their movement, as the Shaker buildings and furniture have (the Shakers were also without children as I recall)! Indeed, I have also heard it said, in reference to some butt-wrenchingly murderous chairs at one congregation -- "They're part of our test for membership, to see if you're Stoic enough to be a UU". No, it wasn't a joke.
But not everywhere, and not every UU fortunately falls into this one-sided, left brain only camp. One of my favorite Unitarian moments was in a small congregation where five women happened to give birth round about the same time, and had taken to sitting at the rear of the sanctuary together with their babes, breast-feeding as needed.
Following one service an elderly gent approached me with the gentlest of complaints. "Um ... you know I do welcome the young people to our congregation ... but I have to say ... during the prayer this morning ... with all that feeding going on ... the silence was a bit too gurgly and snuffly even for me." We did find a wonderful solution, however. He began sitting at the front.