I decided to watch episode 1 of this on a whim the other day. Here is what I think of it.
The Warrior Princess and the Barbaric King bears an ideology that is so nakedly reactionary that it feels like a sermon written by tradcaths. Beneath a bunch of typically generic fantasy slop of swords, monsters, and poorly written political intrigue lies a relentless message: being an independent woman is wrong, ambitious women will become unhappy, and a strong woman will ultimately fail and be conquered for her own good. That sounded like AI but I promise I'm just a shit writer.
The episode begins with the strong warrior princess in chains and captivity before a cliche flashback to how she got here.

Immediately losing a battle with her entire army vs "barbarians" (the neighbouring territory). Upon losing the leader determines she is hot and therefore he will take her as his wife.


She is treated nicely by this "barbarian" in captivity for the rest of the episode, but is ultimately set to become his wife. We're also treated to several flashbacks of her time at a dinner party at the kingdom where dozens of people both men and women alike told her she should just know her place as a woman and shouldn't risk her life fighting.

The episode is clearly a setup to her falling for the barbarian and learning "her place" over time. That essentially everyone around her was correct all along but they were mean about it.
1/10, strongest right wing ideology I've ever seen in an episode 1, the clear message being "girl boss bad" and "must learn her place at hands of a real man". Beats Shield Hero for me.
Hate this shit. I will not watch anything else to determine where it goes but I'm basically certain that she will slowly fall for this big manly barbarian and learn her place as a woman.
EDIT: Oh yeah this shit is on Crunchyroll too so millions of kids are probably being filled with this shit.

And so far, I don't think that's what this is selling.
spoiler
The warriors of the village line up to get their asses kicked by her. She is acknowledged as being the strongest amongst them. The romance is interwoven with her continuing to be a girl boss and fretting over how to help her people when all she knows of the barbarian lands is lies.