I think it's important to point out that unlike other forms of social privilege which are usually discussed -- white privilege, male privilege, cis privilege, ... -- childless privilege is not usually an element of one's facticity, i.e. one does not choose to be black, female, or trans, but for many people, having children is a choice.

Of course, not all people are able to conceive children, and not everyone who bears children does so consensually. And of course, just because someone's choice imposes a burden on their lives and relationships with other people, it doesn't mean that others should not be compassionate towards that person. I do not have children but one of my colleagues does, and I am very happy to make concessions for that as needed, I just consider that an issue of being flexible and treating other people decently, not an issue of privilege per se.

Side note: almost everyone I talk to who want kids defaults to wanting to conceive their own children, instead of adopting. I would argue that adoption is a greater net positive that conceiving new children because it does not increase the population count (which has net negative effects ecologically) and it is providing parents to a child which would otherwise have none. I think I would also find adopting more personally rewarding as well, for those reasons. I wonder why other people do not seem to consider the option as well: is it not heavily promoted enough, or is the appeal of propagating one's genes just so appealing?