Sometimes we make things too complicated... Let us go back to basics and consider a simple question..... Can a doctrine (the political question doctrine) trump a sworn oath? I don't so, A Supreme court ruling on The constitutional eligibility for the highest office in the land is a necessary result of the sworn duty of each justice to uphold the Constitution. If they do not accept this case, why are they there? Thew need to do their duty and not be cowards.
The SCOTUS decisons that support the political question doctrine go back to the founding of our Country — long before the start of the Republican Party. This is less partisan than you may want to think.