On an American scale, Joe Biden is not right wing. He is center left. He is socially left wing, supporting lgbtq+ rights, and abortion. He is also economically left wing, supporting unions and green energy.
A Conservative Democrat isn't a term for a centrist Democrat, it's a term for Conservatives registered/running as a Democrat. They are most Drmocrats in ancestrally Drmocratic states like WV and Kentucky.
I mean, kind of, Conservative Democrats are usually moderate Conservatives, but Biden is still farther left than that, look at his environmental programs, the Inflation Reduction Act, and Amtrak funding.
What's with the banner being porn