The phrase "Sunday best" typically refers to one's best or finest clothing, particularly when attending church services on Sunday. The phrase itself is not inherently racial, and its meaning does not have any racial connotations. According to the Indianapolis Recorder Newspaper “The tradition dates back to the Jim Crow era. Domestic workers were usually allowed one day off a week, and for many that day was Sunday. They would use their hats and clothing to express themselves as individuals at Sunday church service. This tradition is seen today through people, especially women, continuing to dress up for church.” 

However, it is possible that in some historical contexts, the phrase may have been used in a way that excluded certain racial or ethnic groups from participating in certain events or activities. For example, during the era of racial segregation in the United States, African Americans were often excluded from certain establishments and events. In such contexts, the phrase "Sunday best" might have been used to refer to the clothing that was expected to be worn by white participants, while African Americans might have been excluded from attending altogether. 

Overall, it is important to consider the historical context in which a phrase like "Sunday best" might have been used, but in general, the phrase itself is not inherently racial. This phrase is used across various cultures and ethnicities and is not specific to any one racial group.