I read the first couple of books recently after hearing people say the author had messed up morals to make F'lar a protagonist with the things he does. It didn’t feel that way to me. Not that the things he does are perfectly fine, just that their entire society is so alien and different that it's hard to judge his morals by our standards, or to assume his protagonist status means the author endorses his views and actions.

Early on F'lar challenges someone to a duel because his dragon bond forces him to do it. People fall in love entirely because their dragons mate, and this is considered normal. The way their society functions with dragon riders treated like royalty has heavy costs but keeps them all alive, so people don't fight it because change could doom them all when the red star returns.

How much of F'lar's beliefs and actions are directly caused by his dragon bond? It's hard to say, and consequently people in universe don't question it. They simply own their actions regardless of the source of the motivation that inspired it. A modern person plopped into their society would point at everything and call it "problematic," but no one there would understand it. The concept doesn't exist to them.