Quote from @V.G Jason:
Inside liability protection for LLC is the same in every state.
Outside liability protection for LLC depends from the state.
Some states have charging order protection as sole remedy for single and multi member LLC. WY is one of them.
Some states have charging order protection as sole remedy for multi-member LLC only, but not for single member. FL is one of them since Olmstead vs FTC.
So using your holding LLC in WY will give you outside liability protection for all the sub LLC owned by it in other states.
In my setup, I have one multi member holding LLC in WY. I also have one C-Corp acting as management company. This C-Corp is a 1% member of the WY holding LLC, so it is technically one of the owner of the properties titled in the sub LLC, and as such can manage them without needing a property manager license in some state.
Using a C-Corp for the property management let me get all the fringe benefits you can get with a Corp (health reimbursement plan, solo 401k, deduct all investment expense). I can choose how much active income my C-Corp makes to match its expenses. The C-Corp is public and I am the face of the corp. But for the tenants I am only the property manager, I can always blame the 'owner' for the rent increase. In Florida, the lease can be signed by the property manager and the owner does not have to be disclosed. In some states, the lease need to mention the name of the owner, but that would be an LLC where you can't track the beneficial owner as it points out to an anonymous WY holding.