Hubble is in space. They just pointed it somewhere and said “don’t move” (well, multiple times and stacked, but the effect is the same). The galaxies themselves are so far away their own motion is way less than a single pixel.
There’s no such thing as a fixed position in space.
The motion of Hubble (and basically everything inside the Milky Way) relative to the galaxies in that picture is ~250,000 km/s, or 0.83 c.
At this speed, it would take ~100,000 years for the galaxy to move its own length, and even then the movement would be in a direction which doesn’t cause much blur.
To be clear I meant is it in a fixed position relative to earth? I know if you’re photographing galaxies, they move so little relative to us that they might as well be stationary. But isn’t Hubble in an orbit?
Motion on the scale of “orbit” is utterly irrelevant on these scales. Rotation around an internal axis is the only thing which matters, and that’s something space telescopes are designed around.