If x87 and MMX registers don't support renaming then that means that they can't support OOO and speculative execution of these instructions. This is possible but seems unlikely to me.

That is, even though not a lot of x87/MMX code is executed these days (and even less is written) I would be surprised if the OOO/speculative-execution of the processor gets halted whenever these instructions are encountered.

Note that x87 instructions still get used in most 32-bit programs because the x87 registers are the defined way for functions to return floating-point results.

Which is to say, citation needed.