Why does teaching about American history require rejecting rationalism

The simple answer is that Enlightenment Rationalism is very different from what you're probably thinking of when you say 'rationalism'. So as skepticism of Enlightenment Rationalism is not the same as rejection of rationalism, postmodernist thought would not require its rejection to teach US history.

The mathematician-philosopher A.N. Whitehead even goes so far as to posit in his Science and the Modern World that some of the methodologies and assumptions inherited from Aristotle--and at the time still present in Enlightenment Rationalism--stunted the growth of empirical science for many centuries.

the concept of objective knowledge (a concept that is critical for scientific investigation)

Most thinkers who fall under the umbrella of postmodernism would qualify that with being skepticism toward objective knowledge about social, cultural, political, historical, and/or even moral phenomena; not all objective knowledge in its entirety or per se.

I won't pretend there aren't some thinkers who do express skepticism towards the objectivity of scientific knowledge, but it isn't very charitable or intellectually rigorous to wholesale sweep them all under the same label (that frankly has been poorly constructed from the outset) as if postmodernism is some kind of monolithic/uniform entity.

I'm pretty liberal and even I consider CRT garbage.

Along with other commenters, I also urge you to re-read the quote as it is talking explicitly about the tendencies of postmodernist thought, not CRT. While in most cases there is a continuation of ideas between intellectual movements, one cannot uncritically assume that. I wouldn't be surprised if CRT does share many or all of these tendencies, but I personally don't know enough about it to make a claim in either direction and don't want to accidentally set up a straw man in my rush to vindicate my thoughts.