Extremely unprofessional!
So, I work in professional services! Out of my clients, a good share are power-tripping egomaniacs. Some are blatantly incompetent. There are those, who try really hard but fail miserably because they don't grasp how office politics work. And those who (ab)use their professional relationship with me and my firm to point fingers and assign blame.
It's just the job! And that's okay! We get compensated handsomely for "hurt feelings"!
That said: you NEVER, NEVER EVER throw your clients / business associates under the bus! If needs must and someone or other needs to look like the idiot: it's you! ALWAYS!
And, no, it doesn't matter if it's the King himself, H&M, Beyoncé, or the village idiot!
That's just "professionalism"!