Final answer:
The Montreal Expos moved to D.C. to become the Washington Nationals in 2005, alongside a growing awareness in sports about culturally sensitive team names.
Step-by-step explanation:
The team that moved to D.C. to become the Washington Nationals in 2005 was originally the Montreal Expos, a Major League Baseball team based in Montreal, Quebec, Canada. The move was part of a larger trend in professional sports where teams have been reconsidering team names and mascots that may be considered offensive or insensitive, particularly those that reference Native American culture and history.
The reference information you provided highlights the sensitivity around team names and mascots, particularly in reference to the Washington Football Team and the Cleveland Major League Baseball team. However, the question at hand regards the Montreal Expos' relocation to become the Washington Nationals, and is not directly related to the name changes driven by cultural sensitivity that the information provided focuses on.