[JeepHammer]

Is it ok to use gray water for irrigation?

Most of the time, YES.

If you use 'Anti-Bacterial' or 'Anti-Microbial' soaps, then I wouldn't use it for a garden.
Garden soil and the roots of your garden plants are completely reliant on bacteria and microbe colonies to find, break down and metabolize nutrients in the soil, and the 'Killer Soaps' will impede or stop that transfer making your garden a dead zone.

It's real rough on septic systems also.
That rely on the same kind of bacteria and microbe colonies to break down waste material.

So if the package says 'Septic Tank Safe', it's probably safe for your garden.