It has to work well to be believable. However, there are endless issues to which they are forever presenting other theories to explain these issues away. Dark matter has been a problem for 90 years. It's hilarious, and it's a dead-end theory which many physicists are distancing themselves from.
Special relativity was invented to keep the Earth moving, no matter what the experiments showed. For the first time, ether was said to be nonexistent.
Here, speed of light is a constant that never changes. To get these measurements, we need to increase the increase the length and mass of a moving object, and dilate the time.
General relativity makes the speed of light variable, but it is at odds with special relativity in that "space without ether is unthinkable" (direct quote).
So when a problem comes up, they will selectively apply one or the other depending on which will provide more of a believable answer that fits their theories.
I for one don't believe in the speed of light as described. Light is perceived, and I believe it is an excitation of ether which is the background medium that is ever present which produces light. I no longer believe in the accelerative expansion of a universe.