Owning rental property in, or more accurately, transferring title to an LLC is preferable in my opinion to isolate that property from other property you own / your personal assets should someone bring suit against you as the property owner. A common instance would be personal injury on the property where perhaps you were under-insured or negligent in maintaining the property. The problem however is that a standard residential mortgage contains a clause called “due on sale” or an “acceleration clause” which grants the mortgage holder the right to call the note due upon transfer or sale. This provision is boilerplate in all non-assumable mortgage contracts. Keep in mind that it’s a contractual right and not a law, thus they do not need to enforce it, but they may. I suppose one may contact their loan servicer to request an agreement reaffirming their personal liability to the note, but releasing title to the LLC.
In short, if you have a residential mortgage its ill-advised to transfer title of the property to an LLC without gaining written approval from the lender. Generally speaking, if you still have a lien (mortgage) on the property don’t transfer ownership to an LLC. Assuming the property is owned free and clear I would suggest working through an attorney on this process to ensure the rules of the LLC are met and documentation is clear and records kept.