How to deal/work professionally with inexperienced non-technical and arrogant product managers in a startup?

I am quite decently experienced overall (4+ yoe), but new to a startup, the tech folks have amazing background and technical expertise however the product teams sucks, the head of product doesn't seem to have experience in product or tech, he is a marketing guy, who have hired freshers for design and product and my god they are really bad, they do stuff in multiple iterations, don't have clarity on anything, don't know basic components of web and mobile user interfaces, and are arrogant as f to their teeth, always bad mouthing , writing long ass paragraphs on slack, every thing they miss in requirements and design is being raised as a bug in my work, and I am kind of helpless here, I have come out as an incompetent engineer in front of the company

Asking senior folks here how to deal with these little shitheads

Leaving the company is not an option as I recently switched,

Please help.

Also I can't punch them as they both are ladies