Cash-out interest on a rental property isn’t deductible IF it’s used for personal use. If it’s put into a business, another rental property, or a different category of investment, it can be deducted just fine.
Essentially, you deduct it AS IF it were the mortgage on the next rental, bought with cash pulled out, or business loan interest.
If you cash-out refi’ed and used it to buy a shiny new car, you’d be an idiot anyway (car loan rates are cheaper than home loans these days) and deserve to pay through the nostrils.