I'm not sure where this idea of a lack of protein is coming from, since you can certainly obtain more than enough protein from food sources other than red meat.
Eggs, nuts, beans (so MANY beans not to mention soy bean), lentils, FISH.
Soy bean alone can provide tons of protein, whether eaten directly, processed into tofu, fermented into curds, etc.
Even if a Japanese person never ate a single piece of red meat in their life, they would have more than enough protein.
For more information on what the average Japanese person ate check out my big post on Japanese agriculture.
I don't know any sources that specifically quantified their strength, however - while there weren't so many sources of meat, soybeans made up for it as a good quality source of protein in east Asian regions.
How are you defining "strength"?
Were fish not available?