This assumes that most of the population does not already get most of their protein from plant food. This really doesn't seem the case, considering what are thought of as "staple" foods in most of the world: wheat, maize, rice, cassava, potato, sweet potato, etc. A diet where most of the protein comes from meat is more typical of developed nations, and then again, only some of them (hint: the US).
This seems somewhat unfair. According to a summary of the relevant research [1], the actual effects of phytoestrogens in humans are not fully understood, and may be different for Asians and non-Asians. Calling it right-wing pseudoscience is excessive.
Not OP, but if we switch all our protein to soy, that could have unforeseen impacts on things like breast cancer risk due to elevated amounts of estrogen. It's why soy protein supplements are generally discouraged.
Like everything else, soy is good in moderation, and we should have a wide range of choices that aren't just soy-based.
There is no evidence that dietary soy intake changes indigenous estrogen production or estrogen blood levels in a significant manor. Quite the contrary, observational studies of humans who get high amounts of dietary soy, findings have shown either no link to breast cancer or lower rates of the disease. East Asian women consume 10x the amount of soy as the average American yet suffer from lower rates of estrogen related breast cancer.
Eating soy every day has no effect on sexual health or testosterone either.
And also because there have been concerns about phytoestrogens in soy. Whether true or not, the former point still stands.