Can an employer fire me without following their own stated procedures and policies?

The issue or question is whether the stated procedues and policies are in an enforceable contract or not. If they are in an employment contract or union agreement, they should be followed as per the contract. If they are in an employee handbook or similar document, they *may* constitute an enforceable contract (an "implied contract"), IF there are no limitations, restrictions, or caveats as to enforceability. If the handlook, however, says anything like--

"Nothing in here constitutes a contract of employment"

"All employment is employment at will"

"Policies may be changed at will"

--then they are not binding.

If there is no enforceable contract, but the policies or procedures are simply ones which the employer voluntarily decided to use, they may change them at will and are not obligated to follow them.