Yes. A patron, visitor, employee or some other person can be injured in a non-profit facility. The club needs insurance for its own protection from lawsuits.
If you want to protect your non profit organization from exposure to law suits, it would be advisable to obtain coverage. Non Profits are not exempt from financial liability.
Automobile Liability insurance, YES. Liability insurance, NO. There are many kinds of liability insurance.
Just one that cover the basic needs, to not expend a lot of money. That way it doesn't loose money paying for insurance.
If you have liability for an accident, you will need to contact your insurance company. If you do not have liability insurance, you may need to pay for the accident out of pocket.
I doubt it but you should contact a local agent and discuss what risks there could be for your group, and if a policy is necessary.
Your need Professional Liability
You need a commercial general liability policy.
You Need General Liability Insurance.
A Karaoke Club is insurable. You need General Liability Insurance. (also remember to pay you music licensing fees (BMI, ASCAP and SESAC in the US, PRS in UK)
There are many types of insurance you will need to own and operate your barbershop. The most important insurance will be liability insurance. Liability insurance will protect you in the event someone is injured on your property.
A commerical liability policy.
You need commercial General Liability Insurance