It was. Those that opposed the Civil Rights Act of 1964 argued that it was a gross violation of every American's freedom to decide who they wanted to work with, to do business with, and even eat with. Southern Democrats, also known as Dixiecrats, portrayed the law as an attack on the “southern way of life” and prime evidence of the federal government's intent to force racial mixing on the South. The idea of a Civil Rights Act stirred old resentments among segregationists. There indeed was a sentiment that “Civil rights for negroes, means less rights for whites”
An excerpt from an archived NYTimes article from 1964 ...
https://www.nytimes.com/1964/09/21/archives/poll-shows-whites-in-city-resent-civil-rights-drive-majority.html
“While denying any deepseated prejudice against Negroes, a large number of those questioned used the same terms to express their feelings. They spoke of Negroes’ receiving “everything on a silver platter” and of “reverse discrimination” against whites.”