It’s normal.

JFK, LBJ, Nixon, Carter, Reagan, GHWB, Clinton, GWB, and Obama all appointed to their cabinet at least one person from the opposite party.

And Harris didn’t say she would appoint a Republican politician. When Obama chose Bob McDonald for Veterans Affairs, people barely noticed he was registered as a Republican. And one of Donald Trump’s senior advisors was Ivanka Trump - who at the time was a registered Democrat.