Philosophical arguments aside, the fact that three justices appointed by Trump are then ruling on whether he should be granted immunity is in itself a conflict of interest that would not be allowed on any lesser court.
That is a good one and in better times might have seen them recuse themselves? Justices have recused themselves in the past for apparent possible economic conflict of interest - don't know about political conflict of interest.
"shall hold their Offices during good Behaviour" is probably what's meant to address political conflict with a specific person: They nominally can't be removed by the person who nominated them.
