Since Universal Healthcare is intending to preventing wealth from determining who can get treated and who doesnt, and wealth is a form of power dynamic, it is a quality that is left.
inb4: parties in any country do not represent principles wholly on the left or the right. The GOP will have mostly right-wing political ideals, and will have some left-wing. Overall the GOP is considered ont he right because they have far more ideals that are objectvely right (as I defined earlier) than right.
So while in europe many right-wing political parties will support UHC, and that is a left-wing principle, the majority of the principles of a right-wing party will be right-wing and thus overall the party is considered to lean right.
There has never and will never exist a party which exclusively adopts right or left wing principles, even if overall the party clearly exists on one side of the spectrum or the other. In fact the is the very reason why the american GOP is farther right than the tories in the UK for example, because the tories adopt more left-wing principles than the GOP does, pushing it farther to the left while still being right of center overall.