> Would a person who supports Universal healthcare, safe access to abortion and reducing their carbon foot print but also thinks immigration is an issue that needs addressing and supports the second amendment be left or right?

This isn't really what you said, you said "right-leaning and Republican" aren't synonyms, not that people don't fall neatly into the left/right dichotomy. The Republican party is objectively the right-leaning party of the US. If you're a journalist that mostly publishes articles aligning with Republicans talking points today, then it is fine to characterize that journalist as right-wing.