298K and 1 atm are commonly used standard conditions, but they are not absolute. You can define whatever standard conditions you like, as long as you are consistent in applying them. If you define ΔG° at a given temperature and pressure, then if you change the pressure at that temperature, ΔG will change but ΔG° will not. However, if you change the temperature, ΔG° will change. If we assume ΔH° and ΔS° do not vary with temperature (actually they do a bit, but often they can be treated as constant over a small range of temperature), then ΔG° varies due to the relation ΔG° = ΔH° - TΔS°.
(I am not now talking about things like "standard heats of formation" that you can find tabulated, usually referring to 298K and 1 atm. I'm talking about the value of ΔG° that you use in the relation ΔG° = RT lnK, and that is ΔG° at the temperature for which you want to determine K. K then reflects how the equilibrium pressures (or concentrations) differ from the standard pressure/conc. at that temperature.)