I don't support doing that myself, but if you look at the US two of the demographics with the highest reproduction rates are Mormons and Hispanic Catholics. Both follow religious prohibitions against birth control. The progressive left firmly supports the right to an abortion as well as the right to use contraceptives so that answers your question.

From a demographic standpoint what's basically happening in the US is atheist liberals are wringing their hands and dying childless as various religious people produce the next generation that will replace them (Muslims have a very high birth rate too).

All that said, the article was about South Korea which has very different politics. In South Korea I don't think there is a big left/right divide over this and the main issue is probably that they're working themselves to death instead of having kids.