I was recommended to do martial arts for good fitness and focus, with the bonus of some self defense techniques. Is this allowed? They claim to be Pareve and not religious.
Martial arts is not a recommended sport activity. For keeping healthy, a different exercise or sport is more advisable.
The idea of martial arts could be permissible (albeit not endorsed) if the following conditions are met:
1) No women in the vicinity where the martial arts taking place.
2) One cannot hurt another person or be hurt (for example taking punches while making a tight stomach) as is done in some of these activities as part of the training.
However, the various current types of martial arts are not well known enough if they are religious/idolatrous oriented (and some certainly are). Therefore one should not try something without it being checked by those who understand in these matters.
Practically speaking, it would only be acceptable to learn martial arts by a Religious Jew who meets these criteria.
However, it is worth noting that the Rebbe in a letter to a school in Miami (printed in מורה לדור נבוך page 168) was not in favor of a student or Chabad school starting karate as a means of self defense or sport exercise, explaining that it has a lot of other connotations that go together with it. It is also not per-se connected with being healthy “והוא לא תורם לבריאות הכללית של הגוף”.