The US isn't going to get to 500 million by 2050. LOL Maybe 400 million at most. Even if China's population decreased, it would still have 1.4 billion in 2050. It just won't be growing anymore and will continue declining.
However, the fact is China's economy will continue to grow because the country is still urbanizing and optimizing its human capital. Current generations of Chinese children are going to be more educated than their Western counterparts and will likely be more productive when they grow up. There is a huge gap between the older generations of Chinese who grew up in deep poverty and were uneducated vs the ones growing up now who are living in a very technologically advanced society and have access to a strong education system and limitless information.
Lastly, for the US to continue growing its population, that means by 2050, the US will likely be 60% plus Non-White considering that the White American population has already been declining for a decade and is actually declining at a faster rate than China's. Meaning that mainstream US society will look nothing like it does today. The White perspective will become more marginalized. A US that has a majority Latino/Asian/Black population will be much less hostile to a powerful China than today's American society which is still ruled largely by White boomers who have an ingrained sense of racial supremacy and therefore, are immediately hostile to China. Most non-White young Americans will probably have no issue with the idea of a powerful non-White superpower like China and many will probably admire China. If you look at opinion polls towards China, there is a massive divide between the opinions of old White boomers and young non-White Americans (who are the majority in America's youth population under the age of 18). Young non-White Americans generally feel neutral or friendly towards China unlike the deep hostility of old White boomers. I can guarantee you that when young Black, Mestizo or Muslim teenagers see deeply racist politicians like Tom Cotton grilling Tik Tok's CEO Shou Chew, the vast majority of them would identify more with Shou than with Tom Cotton. In fact, they'd probably fucking hate Tom Cotton to begin with.
So no, America is not going to be on the same page, it won't even be the same country as it is today. America will become a non-White country and might even produce someone like Brazil's Lula who identifies strongly with the Global South and is hostile to America's largely Eurocentric heritage.
So the change in demographics will have a huge impact. The US won't be the same country.