seems like an odd choice to so emphatically phrase this as a quality of "the left" when there are so clearly many plausible confounding factors (education, wealth, employment status, do you live in a small city apartment, etc.)
Sure enough:
> Arpino & Mogi explored mechanisms behind this reproductive pattern, finding that extreme right individuals were 4–5 percentage points more likely than centrists to intend having a child within three years. This effect persisted after controlling for religiosity, education, and income
You can just grep papers for "control" to check this sort of thing, as terminology is quite consistent.
There are big differences between left and right in fertility (=how many children you choose to have, in demographic discussions) and this isn't at all a controversial claim in social studies. The question is not does it exist or is it confounded but why does it occur - or if you really want, what underlying factors strongly correlated with leftism are the true cause. You can think of that as confounders if you like.