If the change is in a shared library (and not a service shared over the network), it's fine to change all usages at once. Deploying a service wouldn't affect the others.
If the change affects the public interface of a service, then there's no option but to make your changes backward-compatible.
I hope nobody's life depends on the uptime of a web-based distributed system.
But, well, I also expect nobody's life to depend on it. There would be a short window between people getting into that situation and they not have any life to depend on anything.
Well the arm CPUs we use are in general purpose computers as well. Though you are correct, we don't follow the same practices as general purpose computers.
If the change affects the public interface of a service, then there's no option but to make your changes backward-compatible.