SGB, there are millions of children up and down the land doing karate, judo, even kick-boxing, boxing, or joining organizations like Boys Brigade or the navy one which are linked with the military. For the most part, these things encourage self-discipline, and working as a team, and so on. But even if they didn't, and they encouraged aggression or an acceptance of military values, it isn't up to your friend alone to make decisions about her child like this. It would be laughed out of court if you tried to argue your child shouldn't be allowed to go to karate. This is similar, they aren't fighting in the street with swords, they are in a club doing a sport.
I am on the other side of the fence, my husband doesn't want my eldest to take up judo/karate, because he thinks she is quite aggressive anyway, I think it would be the ideal way to channel that and she would love it. But if I booked her into a session, so what? He wouldn't have the right to remove contact from me, her own mother, just because he thought this was out of order (we are married and therefore just have to bicker over it).
If you apply this very wide definition of 'harm' then almost anything you don't approve of becomes harm; feeding the wrong food, using the wrong language, doing the wrong activities. You cannot control the other parent like that once divorced, and to cut her off from a dad she loves over this would be a greater harm than any minor harm caused by her hitting someone in the playground, getting told off by the teacher, and her learning boundaries (the worst that can really happen).
The worst thing here is not the sport/activity, it is the secrecy, and I would be personally having a word with the dad about telling the daughter to keep secrets, and encouraging openness and honesty.
Parenting with two parents involves strong disagreements, over religion, what school, activities, friends, what time they are allowed out, money, this is normal. It is not normal to cut children off from their parents unless they are in really significant danger (by which I mean abuse or neglect or extreme unreliability/emotional distress).