Will a LLC protect an Arizona resident's personal residence and non-retirement brokerage investments?

No, because the LLC must have a legitimate business purpose.  A business purpose would include providing a service, product, or usable space to an unrelated person or company.  Every small business provides a service or product, or both, to the general public, while investment real estate provides a place to live or do business.  

Your personal residence does not have a business purpose and neither does your personal investment brokerage account.          

Arizona residents qualify automatically for a homestead exemption, which protects up to $150,000 of equity even if a judgment creditor forces a sale of the home.  For homeowners with more than $150,000 of equity, I may recommend either a major increase in homeowners liability insurance coverage or transferring the home into an irrevocable Arizona-based hybrid asset protection trust.  Neither solution requires a business purpose to implement.          

Other reasons you should not transfer your personal residence into an LLC are (1) loss of exclusion of taxable gain upon sale of a personal residence, (2) loss of mortgage debt interest deduction, (3) loss of homestead exemption, and (4) possible increase in property taxes.  

Likewise, while some may argue that a personal investment brokerage account has a business purpose, most would not.  Therefore, I would be wary of transferring a brokerage account into an LLC unless perhaps combined with other assets that do have a business purpose.  The safer approach is to either increase umbrella-type personal liability insurance coverage or transfer the brokerage account into an irrevocable Arizona-based hybrid asset protection trust.