A breakdown of United States Supreme Court Justices (In order of seniority):
John Roberts: Republican, nominated by George W. Bush, his judicial philosophy is a mutt between two, Judicial Restraint (The philosophy that all decisions should be made with the intent to ensure they touch as little other laws as possible) and Judicial Deference (Belief that judicial opinions should heavily weight towards existing power structures).
Clarence Thomas: Republican, nominated by George H. W. Bush, infamously slandered by Joe Biden and proto-MeToo'd during Nomination. Proponent of Originalism which states to consider the constitution in the meaning of its original founding and the amendments to it in the meaning of their founding. Considered the most conservative of justices on SCOTUS. Also a prponent of Natural Law, but more on that under Gorsuch.
Stephen Breyer: Democrat, nominated by Bill Clinton, his legal philosophy is that decisions should be made int he light of those choices which most encourage participation in government decisions. General sides with the democratic judges.
Samuel Alito: Republican, nominated by George W. Bush, is the one whose orders were ignored in Pennsylvania, is a "Practical Originalist", effectively see Thomas above, but add in a level of pragmatism that how the founders saw things is not always viable in a modern world.
Sonia Sotomayor: Democrat, Nominated by Barack Obama, I can't find -anything- on what her Judicial Philosophy is supposed to be, but her decisions generally fall in line with proponents of a "Living Constitution", a philosophy stating that original intent is less important than ensuring that the constitution remains up to date with modern culture.
Elena Kagan: Democrat, nominated by Barack Obama, see Sotomayor for judicial philosophy, its an exact match.
Neil Gorsuch: Republican, nominated by Donald Trump,. MASSIVE prponent of Natural Law (And a minor in Originalism), Effectively a philosophy out of the Renaissance, it says that all men are imbued with Natural Rights, and that all judicial decisions must be made to minimally impact and to reinforce said rights.
Bret Kavanaugh: Republican, nominated by Donald Trump, dragged through the -mud- during nomination, a proponent of Judicial Restraint.
Amy Coney Barrett: Republican, nominated by Donald Trump, very religious, newest judge with a bit of a cloud over her nomination, massive proponent of Originalism as she learned it under the prior most conservative SCOTUS judge, Scalia.