On the tin: significantly slow and delay the Americanization of the 'first wave' of predominantly European immigrants. The goal is an America where well into the 20th century, 'ethnic' immigrants and their descendants still largely live within their social networks. German and Scandinavian newspapers survive long enough to evolve into TV or at least radio across the Great Plains, matchmakers are still consulted by millions of Yiddish-speaking Jews in New York City, Italians keep their folk Catholicism alive and well to the horror of the nativists, 'Little Polands' comprise entire counties in the Upper Midwest, and New England is somehow even more Irish and proud than it is IOTL.
Something likely has to be done about Teddy Roosevelt to make this happen, but I think that going further back would be more effective: kill Horace Mann before he gets involved in public life. He practiced what he preached, transforming education into something that should be supported by the state government as a public, secular institution to impress a common civic identity onto American youth. Without him proving his ideas successful in Massachusetts and spreading them to the Whig Party, this should at least delay the public school system as a melting pot for several decades in time for turn-of-the-century mass immigration. Once they're in by the millions, many public officials without a proven notion of secular public education could shrug at the issue, asking little more of them than obeying the law and paying their taxes. Without the government actively inviting them into 'American' life, the immigrants and their children are likely to follow the existing precedent of American education, building and operating their own schools specific to their faith and mother tongue. If the private-sector skills and trades essential to any society (doctors, mechanics, restaurateurs, etc.) are still being passed down to children getting an education in the language of the old country, that kills off most of the environmental 'pull' into the majority 'just American' life. Thus integration will still happen, but only at a crawl when an individual wants to marry out, suffers disgrace or a falling out with their community, or actively pursues a career in the government at the state or federal level.
Something likely has to be done about Teddy Roosevelt to make this happen, but I think that going further back would be more effective: kill Horace Mann before he gets involved in public life. He practiced what he preached, transforming education into something that should be supported by the state government as a public, secular institution to impress a common civic identity onto American youth. Without him proving his ideas successful in Massachusetts and spreading them to the Whig Party, this should at least delay the public school system as a melting pot for several decades in time for turn-of-the-century mass immigration. Once they're in by the millions, many public officials without a proven notion of secular public education could shrug at the issue, asking little more of them than obeying the law and paying their taxes. Without the government actively inviting them into 'American' life, the immigrants and their children are likely to follow the existing precedent of American education, building and operating their own schools specific to their faith and mother tongue. If the private-sector skills and trades essential to any society (doctors, mechanics, restaurateurs, etc.) are still being passed down to children getting an education in the language of the old country, that kills off most of the environmental 'pull' into the majority 'just American' life. Thus integration will still happen, but only at a crawl when an individual wants to marry out, suffers disgrace or a falling out with their community, or actively pursues a career in the government at the state or federal level.