If the spaceship's Physicist happens to be hanging out of one side of the ship, and he measures the speed of the photons as they pass him and leave the ship, he'll see them passing him at 'c' ... the speed of light.
When those photons pass somebody who happens to be in their path, and he decides to measure their speed, he'll see them move past him at 'c' ... the speed of light.
It doesn't matter whether the observer who measures them is moving, or at what speed.
And it doesn't matter what source the photons come from, or whether the source is moving, or at what speed.
And it doesn't matter what the photons' wavelength/frequency is ... anything from radio to gamma rays.
The photons pass everybody at 'c' ... the speed of light.
Yes, I hear you. That can't be true. It's crazy. Maybe it's crazy, but it's true.