First of all, I always thought the whole “The environmentalists are all really trying to promote their secret agenda of…SOCIALISM!” (DUN DUN DUUUUN!!!) was just a silly right-wing meme.
More substantively, I’m not wildly overfond of trying to settle philosophical or political debates by citing the dictionary, but I do think we need to define our terms here:
“Environmentalism: advocacy of the preservation, restoration, or improvement of the natural environment.”
“Capitalism: an economic system characterized by private or corporate ownership of capital goods, by investments that are determined by private decision, and by prices, production, and the distribution of goods that are determined mainly by competition in a free market.”
“Socialism: any of various economic and political theories advocating collective or governmental ownership and administration of the means of production and distribution of goods.”
Lord knows, the Union of Soviet Socialist Republics had a pretty terrible track record of “preserving the natural environment”; in addition to Chernobyl, the U.S.S.R. wound up creating one hell of a lot of (in American terms) “Superfund sites”, as did places like Czechoslovakia. Alternatively, I don’t see why you can’t have private or corporate ownership of the “means of production” and private, for-profit “determination of the prices, production, and distribution of goods”, and not also have policies aimed at “the preservation, restoration, or improvement of the natural environment”. I’m not arguing for the glorious “invisible hand of the market” to do everything here; I think we need laws and government regulations, but I don’t think “laws and government regulations” equate to"state or collective ownership and administration of the means of production".
Even if you just want to focus on the population issue; to some extent, some kind of “invisible hand” does actually work there: People in wealthier societies actually very often have fewer children than people in poorer societies. A huge factor in getting birthrates down is educating girls and giving women more control over their own lives (which all seems perfectly compatible with “capitalism”). Moving away from “invisible hand” remedies, “welfare state” programs–but still not socialism–like “old age pensions” (Social Security) tend to make people want (or need) to have fewer babies, since they don’t have to “have enough kids to make sure at least one is still around and able and willing to take care of me in my old age”.
Even in terms of more coercive population policies (or at least policies involving state intervention), “lower population” and “socialism” have nothing much to do with each other. Communist China had its (in)famous “one child” policy; but the Socialist Republic of Romania under Ceaușescu was sort of equally infamous for its pro-natalist policies restricting access to birth control (contraception and abortion); Ceaușescu wanted more workers and soldiers to build socialism!
So, all in all, the quotation in the thread title seems like a total non sequitur to me.