I'm a martial arts instructor. It depends on how bad the tear is and what you are hoping to perform. If you're only walking through forms and teaching, that's different than fighting, jumping and doing tournaments. After a tear your knee will never have the same stability until the ACL is reconstructed using either a section of your own tissue and bone or from a donor. If you choose to use your own, you will have extra weakness and you will need rehab for the ACL, and for the site where they removed tissue and bone to graft.
I just had mine done 10 weeks ago and I used donor tissue because I didn't want to harvest my own and then have to rehab that weakness in addition to the ACL rehab. It takes at least 6 months to get back to full activity, but more commonly a year.
If your ACL is not torn all the way across, and if you are only doing light activity, you might be able to get away with strengthening the leg (hamstring, patellar tendon, quads, calves, etc). My surgeon had told me to do that and hold off as long as I could due to the down time involved in ACL reconstruction. Also, at some point, you will probably develop at least a little arthritis from the surgery itself, even if it doesn't hit you until years later.
ACL reconstruction has its drawbacks, but it's really the only solution (unless your cartilage is gone and they need to do a total knee replacement). On the bright side, professional athletes have this surgery and often go back to playing pro sports. Even with total knee replacements I've seen people go back to doing karate. Judo might be a lot tougher on the knees.
They might be able to get away with it for a little while, but it would not be a good idea. With a torn ACL, your leg has very little support and very easily will "give out" from under you if you move in certain ways.