None, probably, if you’re taking the definition of “open hardware” where you have full access to the microcode running on it and can modify it yourself.
Microcode is necessary to decode instructions. When you give the CPU instructions, it decodes them into microcode which is what actually specifies the sequence of electrical operations required to process that instruction.
Right, but it wouldn't be possible for a modern CPU (for example: how would you retain compatibility with older architectures? how would you patch it if you find a critical bug in an instruction?)
Furthermore the parent was asking about having no microcode running on the CPU which is what I was speaking to. A CPU designed to use microcode can't be run without microcode. But yes, it is of course possible to design the CPU to not use microcode in the first place.