Earliest archived use of the term on 4chan was from 2017, several years after soylent meal replacement shakes hit the market. Soy was also being used in various other vegan and/or processed foods at the time, but soylent was particularly conspicuous due to it having soy right in the name.
Regardless of which particularly product prompted this, the point is the meme is new but westerners not eating soy is not new and cannot be attributed to the meme, nor is the meme even about asians. The memes mocked white guys in the west who eat soy products, particularly soylent. As for the general aversion to eating soybeans, read the Wikipedia page for soy. It has a short history of soy consumption in North America since the introduction of the beans here in the 18th century. For most of their history in North America they were raised almost exclusively as animal feed. This wasn't because of a meme that didn't then exist, nor because anti-asian racism; it simply wasn't considered very good to eat. America got the bean itself from Asia but not the culture of tofu production and consumption. In the 20th century methods of processing soybeans for human consumption started to be developed in North America, but it would take several decades to gain any appreciable traction.
The "soybeans are effeminizing" train of thought only came about very recently in response to soybeans actually being consumed now in North America. The memes about "soyboys" exclusively featured white men who were usually skinny or skinny-fat, office workers who lacked physical strength, not laborers, usually with thick-rimmed glasses and an enthusiasm for immature interests like video games or saturday morning cartoons. The memes were about these sort of white men, not about Asians.
Tldr: these memes weren't about Asians and neither were they the reason it took so long for soybeans to catch on. That's completely ahistorical, wrong by centuries.