This. I don't have children and don't think its a good idea do to what humanity is doing to the planet, regardless of which element of humanity is to blame, but my other family members have children as do my friends and neighbors. Im not going to proselytize to them or encourage society to disallow it. I may not want it subsidized though, but even that there is often times no choice. For example while people may be bad for the planet in general, ignorant people is worse, so im gonnna want education funded and that same thing plays out for a lot of things.
The subsidies have an ontological value in that they improve the quality of life for the child. So removing subsidies will actively perpetuate and increase the very systemic issues that many antinatalists care about in the first place. You address this too, I'm just expressing agreement that simply removing chiodcare subsidies is not ethically simple even for staunch antinatalists.
In general governments ought to be working to support the people they represent. To me it seems an antinatalist who's goal is to reduce suffering would want to introduce things like a basic income or some such to improve the quality of life of those who do exist, not further take from those who have yet to be.