The problem an AC can create for electronic units is that, for a few seconds as it starts up, the AC motor pulls a huge current and that can drop the voltage because of resistance in the wall wiring. That resistance is normal (unless there is a real wiring flaw.) So some electronics experience voltage sag for a few seconds every time the AC starts. The second, less likely situation comes up if your circuit already is heavily loaded. In those cases the start-up current just might push the total circuit load over the limit and cause the breaker to trip out. Then your electronics experiences a complete power failure. If that happens just when certain tasks are under way (such as a disk write) you will see damage in the form of corrupt files, etc.
A Surge Protector does not help this - it's designed for fast high voltages, not sags. The UPS suggestion would do it. If all you want is protection from short voltage sags, a smaller unit that does not keep things going for a long time is OK. Just be sure it is the type that is always supplying power, not the old type that switches itself over after the power fails.
The other alternative is to set the AC up on a separate circuit (preferably with little other load on it). You'd need to find an outlet that does not turn on and off when you trip the breaker for your electronics units. You might need to run a heavy-duty extension cord (one that says it can handle an AC) to reach that outlet. The advantage is that the heavy current pull and resulting voltage sag will happen on different wall wiring. It is unlikely the voltage will be pulled down at the bus inside the breaker panel, so you would prevent causing the problem where your electronics are plugged in.