Bill of Rights Socialism

While I believe that the CPUSA’s ideological positions are pretty solid, I’m kinda confused by the concept of “bill of rights socialism”, which advocates for the US bill of rights to be maintained under socialism, and adjusted in order to align it with socialist concepts. While I can see the concept here, it does confuse me why the CPUSA would, as a Marxist Leninist organization, advocate for a bourgeois-democratic constitution to be upheld under socialism. Am i misunderstanding this?