When financing a new vehicle, can a dealership add on disability insurance as a requirement to purchase?

Yes, the dealership may add this, as long as it is discussed or required prior to your signing the contract to buy the vehicle. Selling anything is a voluntary act; sellers may add requirements or conditions to protect legitimate interests. Since your disability could prevent you from paying the financing on your vehicle, it is a legitimate request that you have disability insurance to ensure that the car will be paid for if you are disabled. Again, though, they must ask for this "up front"; if you've already agreed to buy the car, they cannot after the fact add an additional requirement of which you were unaware when you signed. However, by disclosing this up front, prior to agreeing to buy the car, you have the chance to walk away and buy from a different dealer, if you choose.

The lender that you want to finance the car's purchase can legitimately require that you place a disability insurance policy as a condition for the loan where it would be the beneficiary if you become disabled and cannot make the car's monthly payments.

The lender has a legitimate interest in making sure that its payments you owe to it over time for the car will be paid on time. The requested disability insurance policy is a reasonable request of you and such policies placed in car loan situations as yours are customary.

You can try and negotiate around the requirement of the disability insurance policy. However, the dealership can remain firm in its demand. If so, it is up to you to make the final decision o the required policy.