System Management Mode is not the only thing that makes x86 bad at hard real time. The unpredictability of the execution speed due to caches, pipelines and so on makes x86, and any other high-end processor, bad at real time. All these features that make a processor fast on average also make the worst case difficult to manage.
The current generation of ARM chips is divided in three series: Cortex A for high-end microprocessors (the closest thing to x86), Cortex-R for real-time applications, and Cortex-M in a microcontroller profile. The Cortex-R does not have an MMU (some have an MPU) but may have a cache. It is used in many real-time applications (ARM tries to compete with DSPs, fairly successfully).
The ARM architecture itself does not define anything like SMM. It's possible that chip manufacturers add something like it, you'd have to look at the manufacturer's documentation.