Not for any reason. Even in at-will employment states, you cannot fire someone on the basis that you discovered they are Christian (or Muslim, or Polish, or an Army veteran) and you don't like Christians (or Muslims, or Poles, or vets). Some are federally protected categories (termination on the basis of race/ethnicity/religion/gender is banned nationally under the Civil Rights Act of 1964), while others are prohibited by state laws. The status of firing someone because they are transgender under federal law is in flux; the EEOC issued an interpretation in 2012 that the 1964 ban on gender-related employment discrimination covers employment discrimination on the basis of transgender status, but I'm not sure whether this has been upheld by courts.
Of course, you can state no reason, and avoid leaving evidence of your real motivations, which might make it harder to prove: if you fire someone because you discovered they're Polish and you hate Poles, they can only win an unlawful-termination suit if they can prove that was the reason.
In the United States there has been a long history of discrimination against national origin, especially of recent immigrants. Poles were just used as an example here of a national origin.
True, but U.S. anti-discrimination law rarely speaks directly about race, and instead uses the broader phrasing "race, color, or national origin", which covers pretty much anything race- or ethnicity-based.
Of course, you can state no reason, and avoid leaving evidence of your real motivations, which might make it harder to prove: if you fire someone because you discovered they're Polish and you hate Poles, they can only win an unlawful-termination suit if they can prove that was the reason.