I believe that there could be a problem here by using the term "racism" because "racism" has a very complicated and nuanced definition and varies widely in its application as a result.
Addressing a group of non-white people as a white person claiming that racism is evident in their speech implies that the level of discrimination they've displayed is indicative of a belief in systemic racist ideology. Racism does not affect white people because racism is a belief that supports continuing systemic violence against people of color. Racism does not harm white people at a systemic level. Racist ideology comes from white people because it was designed and created to keep races other than white people at a disadvantage in society. It is simply disingenuous to equate your Asian coworkers making assumptions about where white people live (well, mostly Appalachian people, which I will address shortly) to racism.
You may disagree with my definition of racism. They may disagree with my definition of racism. Others here may disagree with my definition of racism. The reason why I address it here is that I believe there are better ways to approach this situation described by the OP than using the term "racist."
All that aside, here's some scripts I would recommend.
This is discrimination. Addressing discrimination specifically and calling it by that name avoids any contentious topics about what it means to be racist.
In your case, I would try to say something along these lines:
"These assumptions about the kinds of people who live in the South is hurtful."
"I don't think it's fair to categorize the South based entirely on stereotypes."
"It bothers me that you've implied that poor white people are trash."
A further note:
In my discussion of racism, I mentioned Appalachian people. Appalachian people are the people who most refer to as "rednecks" and "white trash." These are generally poor people living along the Appalachian mountains (hence its name). These are people living in parts of Pennsylvania, Ohio, Virginia, Kentucky, Tennessee, the Carolinas, Georgia, Alabama, Mississippi, or the entirety of West Virginia.
Most of the states mentioned above are among the poorest states in the country. Mississippi, West Virginia, Alabama, and Kentucky are four of the last five states in terms of income. West Virginia's most common jobs include: roof bolting, mining, shuttle car operators, mine cutting and channeling machine operators, continuous mining machine operators, helpers / extraction workers, wellhead pumpers, etc. These are extremely physically demanding and also pay poorly. The people there are poor and face the effects of poor welfare legislation, safety regulation, and environmental pollution regulation.
This is information that isn't very well known; it's just assumed that "white trash" is just equivalent to poor people or "country people", but when people talk about the stereotypical "red neck", they're usually describing Appalachia. If you wanted to take the time to educate your Asian coworkers about how they've miscast the "South" as Appalachia and the problems that many people in that area face, that's also an option.