Well I decided to call my two sisters, who do not have children (I won't say child-free because they wanted to, but couldn't) and asked their opinion.
I was really surprised to hear them say that they agreed that employees w/o children are excessively called upon to cover for those who do.
One sister commented specifically that she was expected to travel more, work longer hours, and cover holiday periods, because she did not have children.
I asked her if she didn't feel that being able to travel and work extra hours hadn't improved her career - and pointed out that I would consider traveling for work to be a perk, not a burden. She acknowledged that yes, in some ways her career did advance because she had more flexbility - but was still stuck on the holiday issue.
The other sister said that, speaking as a boss, it frustrated her to have women asking for time off for various family activities, leaving her to worry about how to keep the office covered. And if she said "no", to such requests, employees became resentful and surly.
I did try to point out that employees can be resentful and surly, even if they don't have kids!
It seems to me though, that this shouldn't be an employees w/kids vs employees w/o kids issue.
Employees shouldn't be setting policy - management should. The company should have a policy in place regarding flexible time off that is equitable for everyone. Holidays should be rotated, and travel opportunities (or burdens) offered to everyone who is qualified.