Now, how does this (the principle of equivalence) still hold true?
First of all, I do not profess to have a deep understanding of general relativity (GR). My answer is based on my admittedly superficial understanding. Therefore, I am sure others can answer better, and I encourage them to do so, as it may help me understand it better.
I believe the equivalence principle would still hold true, because I think it in effect says a local gravitational field having acceleration $g$ is indistinguishable from the rocket undergoing an acceleration of $g$. I should think that if the LIGO apparatus were placed in the rocket (it would have to be a very, very long rocket!) and detected gravitational waves, those waves would be due disturbances in the fabric of space time due to non local violent accelerations of large masses. This, however, should have little or no effect on the local measurement of g.
I think the rocket measurement of a non varying gravitational field may be somewhat analogous to measuring an electrostatic field (field due to stationary charge). The LIGO measurement of a time varying gravitational field (gravitational waves) due to violent accelerations of large masses may be somewhat analogous to measuring electromagnetic waves due to acceleration of electrical charge. Both the gravitational waves and electromagnetic waves travel at the speed of light. However, the violent accelerations of large masses would be occurring very far away from the detectors (and the rocket), otherwise the detectors and those operating them would not survive.
Hope this helps.