In-order CPUs aren't automatically immune to speculative execution exploits. ARM's A8 core is an example of an in-order core that was vunable. It's speculative

In-order CPUs aren't automatically immune to speculative execution exploits. ARM's A8 core is an example of an in-order core that was vunable. It's speculative execution that causes problems, and in-order CPUs still do speculative execution during branch prediction. It's just that they typically get through less instruction while speculating. All you need for Spectre is a branch misperception that lasts long enough for a dependent load. However, it's been over three years since ARM have known about Meltdown and Spectre. There is a good chance the A510 is explicitly designed to be resistant to those exploits.