What is the relationship between independent agencies and partisan politics

The relationship is that most independent agencies have a statutory requirement, their member have to be bipartisan (members of different political parties). In this way the President is not allowed to fill vacancies with members of his own political party. However, Presidents usually fill enough vacancies to constitute a  majority of votes on each independant agency commission.

“i think it is very plausible that if there are five votes to end the death penalty, it could be with the people who are on the court right now,” - smith

so basically it is not clearly and consistently imposed