I think it's a great question Warren that at first may seem like it's easy to answer. However, if you think about it a little longer, then it's not always so easy.
I definitely believe that there is a clear answer for obvious things regarding protecting the safety and well being of my child. Thieves that are known to destroy teams, steal from the girls, and will leave my DD (and others) without a place to play, coaches who make inappropriate sexual comments or, worse yet, actions towards the girls that they are coaching, coaches that may threaten or actually proceed with physical violence against the player, coaches that will completely degrade and belittle players on a regular basis - it is easy for me to say that absolutely not. It is not worth going through that for instruction - you can find good instruction to improve your daughter's abilities. You may have to drive further or pay more for it, but in the long run, the total cost is much less in terms of psychological damage (or worse) that could be inflicted from the other type of coach.
Where this question becomes a little more difficult is what I feel is a "gray" area. I think smaller actions can be thought of by some to be damaging to the well being of the child, while others may feel the actions are just a part of sports, life, and "character building." This may very well depend upon the personality the girl themself has. Just as an example - where my DD goes for catching instruction. She responds very well to them. However, they are tough and tell it like it is. He sometimes curses. My DD is OK with it because she knows that they also support her and are positive - way more than they are negative. However, some girls just don't respond well to any kind of negativity - they shut down. Not knocking those girls - it's just part of their personality and they would respond better to a different type of instruction. For some parents, they may feel that taking their DD to him would be bad for the well being of their child, where as I don't feel that way about it at all. There could be countless examples, but I think it's those types of areas of well-being that get to be a little gray.
I also feel that it depends on the age group you are talking about and what the goals of those girls are. At the younger ages, where development SHOULD be the goal and they are also still developing their sense of self, then considering the well being of the girl - even in the more gray areas - is vitally important. You want to develop them skill wise, but also keep the passion for the game. However, when the girls are older, more sure of themselves, and the goal becomes college recruitment - sometimes there are more things in the "gray area" that the girl is willing to tolerate or endure in order to achieve her dream that weren't tolerable at a younger age. As a parent, I still would not allow my DD to play for a coach that I knowingly is going to do anything in the "black area" regardless of her dreams and goals. However, if there are smaller things in the gray area that she is willing to learn to tolerate and it is clear that the team, overall, is going to give the best experience and chance for her to meet her goals, then we would have to consider it. She is older now and I can't protect her from everything (even though I want to). It becomes a benefits vs consequence kind of thing.