If I teach Jiu Jitsu at an academy, can I deduct the academy membership since it is continuous training for my profession?

Perhaps.   Let us provide some background first about self-employment and business expenses.  You mentioned that you teach Jiu Jitsu, therefore, this response will assume you are self-employed.  You may have another full-time or part-time job where you are an employee; however, you can still have a job outside of your work as an employee and still be self-employed.  Thus, if you are self-employed, in other words you are in the business of teaching martial arts classes such as Jiu Jitsu, and you are not performing this work as an employee for someone else, then yes, you can deduct your ordinary and necessary business expenses.  If obtaining an academy membership is ordinary and necessary for you to perform your teaching, then you can deduct such expense.  

If you are performing your teaching work as an employee, then the expenses you incurred for the academy membership would not be deductible.  Unreimbursed employee expenses are no longer deductible as they once were.  

Some additional information about what is an ordinary and necessary business expense might also be helpful here.  According to the IRS, "ordinary" means that most other self-employed taxpayers who work in the same business or trade also commonly pay for these things. "Necessary" means that whatever you spent money on assists you in doing business. In fact, you might not be able to do business and earn money if you didn't make these expenditures. 

This opens up a serious can of worms:

How about being an actor or model who needs to maintain a certain level of fitness for their self-employment?  The same could go for self-employed.. anyone who needs to maintain flexibility and strength to do their job and has had a doctor tell them they need to do XYZ exercises in a gym or pool that they don't have access to at home.

I work in the entertainment field and we all are employees but for like 1day to a few weeks.  I work as a producer  (not an actor as mentioned above) but get paid 1099 and W2 (see HB-85 in CA).  So, now what is self-employed becomes nuts.  We are all freelance but "self-employed" on some gigs and not others depending on what the company decides to do.

My doctor actually told me to swim and do exercises that I couldn't do at home to undo lots of issues and I do have a note.  I'm very tempted to "write off" the difference between a basic gym membership and a membership to a club with a pool and advanced equip have my doctor's note as a back up.  

I suppose TOO if you are self-employed that if the club had business amenities and you networked there, that would be a separate type of business expense and you could just take the whole club?  Or, maybe again some percentage of what you do there that's business and what you do there that's for what your doctor tells you to do there?

There are two questions here: what can be written off as an ordinary and necessary business expense and what can be written off as a personal medical expense. 

Regarding business expenses for the self-employed, it is a little nebulous as to what is considered "ordinary and necessary." If you are an actor and have your hair done for some headshots, that meets the requirement. If you have your hair done because you have to maintain your appearance as you go through life, probably not. Two categories the IRS specifically prohibits taking as business expenses are personal living and family expenses and dues to business, social, athletic, luncheon, sporting, airline, and hotel clubs. Where you draw the line between a personal living expense and an ordinary and necessary business one is a little fuzzy. 

As for personal medical expenses, the first thing to note is that very few people are even eligible for these. Your out-of-pocket medical expenses would have to exceed 7.5% of your gross income before you are allowed any deduction and you would have to be itemizing your deductions. Gym memberships are specifically excluded and cannot be deducted. There is not as much gray area in the medical expenses as the IRS does list a number of includable and excludable expenses. 

@Freelance

What if I drive over the road. I use them for showers and to keep healthy.

Which medical conditions or diagnoses would require a gym membership that IRS would accept?

The IRS only addresses gym membership in the context of weight loss for a specific condition:

You can include in medical expenses amounts you pay to lose weight if it is a treatment for a specific disease diagnosed by a physician (such as obesity, hypertension, or heart disease). This includes fees you pay for membership in a weight reduction group as well as fees for attendance at periodic meetings. You can't include membership dues in a gym, health club, or spa as medical expenses, but you can include separate fees charged there for weight loss activities.

See Weight-Loss Program in the IRS' Publication 502, Medical and Dental Expenses. 

That said, a deduction wouldn't necessarily be restricted to weight-loss issues.  Please see MichaelMc's comments above, as they're right on target.  Membership fees can be deducted only if a doctor has diagnosed you with a specific medical condition, or a specific physical or mental defect or illness, and you have written documentation of this diagnosis. The health club facilities must be used to treat the specific condition, defect, or illness as recommended by your doctor.

@josie0176 

I was diagnosed with osteoporosis in 2022 and was told to do weight bearing exercises to help increase bone density. I joined a gym and work out 5 times a day now. Does this qualify for tax deductible health care?

Yes, this would qualify as a medical expense if specifically prescribed by a physician.

@ynpim