I must respectfully disagree. I am very much with you on recognizing the importance of the language that we use and that we need to build alliances not reduce everything to an Us vs. Them dualism. That said, the term and concept of "colonizer" is important because we can't whitewash the reality of settler colonialism.
The corporations that arrived in African, American, Asian, and Oceanian lands to steal natural resources were colonizers. My ancestors who immigrated from Europe to the United States were participants in settler colonialism. These are historical facts that if we deny them, we are continuing the sins of colonialism.
Whether Dr. King would or would not agree with the use of the term "colonizer," we can look to many other significant scholars who do use that term with great effectiveness. Frantz Fanon is just one example, https://medium.com/politically-speaking/frantz-fanon-on-being-black-2373c50bf92a. Only by acknowledging that we are all in some way descendents of colonialism can we make headway in dealing with the still lingering damage of the colonizers.