Don't underestimate the role of propaganda to vilify the 'enemy' and have the populace rally around the cause. Even so, the general public is quite ignorant on most of the foreign policy stuff and that doesn't stop anything us from getting involved. Containing China is of strategic importance because it's the only country with the economy that could support a navy large enough to rival ours. Unparalleled control of the seas has been the biggest military and economic advantage America has had in the last 70 years. If it becomes necessary, you'll see the government's push to rally the public around 'protecting our allies.'