I can think of a darker reason for the anonymous posting of signs advertising children's "play groups." And that reason is pedophilia.
The fact that they are requesting only white children could be indicative of the naivety of those all too many white folks who live in sheltered enclaves, and who are only too eager to escape from their perceived "horrors" of exposure to diverse populations.
Numerous statistics and demographic profiles that you will find online indicate that an overwhelming percentage of child sex predators are white.
The presumably white people who will be welcoming white parents and their children into these newly created playgroups will be doing so without the parents really knowing who these people are. The parents will know only that these organizers are white, and therefore "safe." Talk about an opportunistic means of leading lambs to the slaughter.
I'm not merely speculating here. I have contacts with local police via my work regarding antisemitism education where I live, and we have found that it's always the same types of people coming up with similar schemes who are (rightfully) kept under scrutiny.
Edited to add:
I read this in the OP's posted link: "The posters lead people to join a Telegram group described as a space for white parents in the Tri-Cities."
Just mentioning that the Telegram app has been cited in numerous police reports as being used by pedophiles for their organized activities, due to the anonymity it provides its users. Once unsuspecting parents contact these "playgroup" organizers via Telegram, they could be directed to meet in otherwise undisclosed places. Even without parents and children physically attending a group meeting in an undisclosed place, the organizers will have the opportunity to gain personal information from respondents about their children, including their home addresses, their children's routines involving home life, attending school, etc.
Any parents who arrange any kind of play date for their child through strangers via a shady, anonymous means such as Telegram, just because the strangers are white (and therefore "safe" in these people's minds) have got to possess a level of stupidity that exceeds even their all-consuming racism, suggesting that they never should had bred in the first place.