I’m not sure how anyone can read Homelander as anything but a right winger.

Its not that he's right-wing so much as his the Good Guy.

His early-show character arc is one of a feckless image-obsessed corporate prop. As the show progresses, he breaks out of the "cucked" liberal mindset and asserts himself as an ultra-nationalist for the benefit of an insecure and gullible media audience. So a right-winger can read Homelander's arc as a kind of Hero's Journey, from captive tool of the (((globalists))) into a fully realized superhero.

So, using a JBP-inspired reading of the material, he starts out as a liberal in season 1 and self-actualizes as a fascist by season 3. And this makes him the show's protagonist, as a result.

the fact that he has an American Flag costume and surrounds himself in American Flag stuff should be a dead giveaway.

He'd hardly be the first liberal to wrap himself in an American flag.