Americans' attitudes towards race during this time affected the country's involvement in overseas expansion in important ways. It allowed Americans to believe that they deserved to take control of various overseas areas. At the same time, it caused some Americans to oppose imperialism.
Americans of the time by and large felt that people like the Hawaiians and the Filipinos were racially inferior. Because of this, they felt no compunctions about doing things like overthrowing the legal Hawaiian government of Queen Liliuokalani or fighting the Filipinos to prevent them from becoming independent after the Spanish-American War. In this way, racial attitudes led to support for expansion.
At the same time, these attitudes could lead to opposition to imperialism. Some Americans did not believe that it would be good for the country if large numbers of non-whites were taken into the country when their lands were annexed. Such people did not want to hurt the US by making more people of inferior races part of the US.