It’s a bloody tough one when Capt doesn’t respond to FO, we all have different SOPs on how we challenge/ respond.
As an FO it no matter what you think it is not easy taking over, yes of course if in direct danger, but otherwise?
Yes it did happen to me a few moons ago, Capt blah blah blah, ending with after x times, “Name” you must go around now, a slow go around initiated. Was it pretty? No, was it safe? Yes. Did we have a post flight chat and beers? Kinda? Were we called to the office after FDAP download, sorta. Were reports put in? You betcha.
No one wants to see a colleague in trouble, SAFE operation is however critical, taking over from a Capt is a major move (I was a very senior FO in my above issue), I have actually never heard or read a report on it and consequences?
Safe flying always comes first, its ok to go around!