This is a weird misinterpretation. Her campaign is seeking to reach a broad coalition, and by focusing on policy issues that matter like healthcare, economic inequality, climate change, housing prices, and childcare, she's addressing concerns that affect people across all backgrounds. When she mentions that her identity isn't a central theme, she's not implying it's 'dangerous' to discuss. She's emphasizing that she doesn't want to be reduced to just her race or gender. Highlighting identity can be an asset, but in an election like this, it's also important not to let it eclipse your policy platform. She's not taking a class reductionist position, and she's not taking one where so-called 'identity politics' is the main driver, and it's for the best.
As for the comparison to Barack Obama, it's 2024. And every candidate's path is different.