Now when we can measure Gravitational Waves, how does the 'Principle of Equivalence' still hold true? LIGO measured gravitational field waves.
The whole thought experiment of Einstein, leading to ‘principle of equivalence’, assumes that there is no way to know inside the rocket that whether its accelerating or things are acting under gravitational field.
Now, how does this still hold true?
 A: 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. 
A: The principle of equivalence is not about extended measurements across space. For example, the gravity around a planet is different from acceleration: it’s different in different places, exhibits tidal effects, etc. 
Gravitational waves cannot be detected at a point. They only can be detected via extended measurements. So they don’t really have anything to say about the equivalence principle. 
A: 
LIGO measured gravitational field waves.

False. To answer your question we need to be more specific: It actually measures the time it takes a beam of light to travel down a long tube, bounce off a special mirror, then come back. And it does this for two perpendicular tubes. The time of flight tells you the length of the tubes, since we know the speed of light very accurately.  Therefore LIGO is an accurate tube-length measuring device.
Anything that alters the length of the tubes will be detected, including the contraction and expansion of space time as a gravitational wave passes. But accelerations of the tubes by mundane sources can also alter the tube length (including wind, earthquakes, local traffic, and farm equipment to name a few).
edited:
Going back to the equivalence principle, place a LIGO inside a rocket in deep space and then accelerate that rocket back-and-forth and side-to-side just like a gravity wave. The LIGO wouldn't be able to tell the difference between this and a real gravity wave, just as the equivalence principle predicts.
A: Yes, the Principle of Equivalence still holds true. 
Actually, the question incorrectly presumes that Gravitational Waves and Gravitational Field are one and the same thing, while they aren't, as is clear from the answers to the below Quora question:
Quora: What is the difference between Gravitational Field and Gravitational Waves?
Reading answers above, it will be clear that in the related thought experiment, the person inside the rocket, NOW, can only measure Gravitational Waves or changes in Gravitational Field, which is not the same as measuring Gravitational Field itself, and, which doesn't cause acceleration but change in acceleration, as is clear from the answer to another question on this site:
Do Gravitational Waves cause a 'Rate of change of Acceleration'?
