As an anti-natalist (more precise would be anatalist, I am not opposing that other people have kids, I just wish they chose not to), let me address that. The point is not everybody to not have kids, but just enough to stabilize or slightly decrease the population.
First, you're assuming that climate denial is genetic and not cultural. Which is a big assumption, and I am in general in favor of nurture argument. (As a side note, by waiting longer to have kids, humans might actually be selecting for kids that are learning more and longer, which favors nurture even more.)
However, even if I take that assumption. If I chose not to have kids, that very much means I do not care about biology and what my genetics want. I am making the decision as a person free of the evolutionary pressure (well, somewhat, because I still care about survival of human race). Therefore, I am not sure why I should be bothered by the evolutionary pressure on other individuals. The truth is, it is going to be their battle. I can only lend them a helping hand (and perhaps an example), and do (what I believe is) a morally correct thing. If they mess up and still act wrong, it's not my moral responsibility.
It is a similar question as to whether or not vote strategically. If everybody votes strategically, you can get a result that no one wants. Therefore, somebody has to sacrifice and decidedly vote not strategically.