Gravity does have an effect on electromagnetic radiation, including radio waves and visible light. According to the theory of general relativity, gravity can cause the path of light to curve as it passes through a gravitational field. This effect is known as gravitational lensing and has been observed and confirmed by astronomers.
When light from stars or other sources passes through a gravitational field, such as that of a massive object like a planet or a black hole, the path of the light can be bent due to the curvature of spacetime caused by the gravitational field. This bending of light can cause the apparent position of the source to be shifted or distorted.
However, in the specific scenario you mentioned, where stars are moving through space at near-light speeds, the effect of gravity on the direction of the light is not the main factor. When stars are moving at such high velocities, the dominant effect on the observed direction of light is the relativistic aberration of light.
Relativistic aberration is a consequence of special relativity, which describes how the apparent direction of light is affected by the relative motion between the source of light and the observer. It causes a "light-bending" effect, where the light from a moving source appears to come from a slightly different direction compared to its actual direction.
This relativistic effect compensates for the gravitational lensing caused by the star's motion through space, resulting in no net deflection in the direction of the light. The combination of the gravitational effect and relativistic aberration cancels out, and the light from the star appears to travel in a straight line from the perspective of an observer moving along with the star.
It's worth noting that this explanation assumes the motion of the star is uniform and that the gravitational field it encounters is not extremely strong. In extreme cases, such as near a black hole, the effects of gravity can become more pronounced, and gravitational lensing can cause noticeable deflection in the direction of light.