You don't say how old your son is and that is a factor in some of this. If you talk to many doctors and experts they really are against head trauma of any kind to younger people and this includes football. While not every kid that plays football or participates in martial arts suffers brain damage there is some reason for concern here I think. Along with age other things like amount and severity of the head trauma, how much and hard the contact on a regular basis in general is, and if certain safety precautions are being followed.
In cases where there has been hard and severe contact on a recurring basis and usually in successive incidents like back to back there is some correlation between brain damage to some extent. This can manifest itself in slower reactions, trouble focusing or concentrating, and worse in severe cases. I have a friend that takes seizure medication every day because of the amount and type of punishment he took as a young adult in kickboxing and Muay Thai fighting because his coaches and the promoter he fought for did not care and did not monitor this and exercise some common sense. So bad things can happen but don't for the majority.
Much but not all of karate in this country is aware of this and takes a cautious approach with it but I have seen some that don't and probably should not be teaching younger people or at all. In something like Muay Thai where the contact is harder and heavier as a rule and on a regular basis there is of course more chance of it. If your son is younger, then you as a parent, should investigate the classes and instructors of any martial arts program he is considering so that you have a better handle on this and not leave it to someone else to determine.
Attend some of the classes when sparring goes on and note their approach to it. If things like head gear and mouth pieces are not used then pass and look for some place that does enforce such rules along with monitoring the amount and type of contact that is allowed and accpetable. I have even had friends who are adult professionals seek out classes and programs in their areas who don't live near me who have had some bad experiences in regards to this so it pays to shop and invesitgate things thourghly.