Newton's law of gravity was inconsistent with Einstein's special relativity because

the distance, and thus the force, depends on the reference frame chosen

time dilation slows the apparent acceleration, reducing the force

mass, and thus the force, depends on the reference frame chosen

Newton didn't know about Einstein

Mass and thus force depends on the reference frame chosen

Explanation:

This can be explained as Newton's law of gravity provides action which are instantaneous at a distance and involves the evaluation of all the quantities at present time or at the instant they occur.

If the body undergoes a change in its mass distribution there will be an immediate change in its gravitational force without any lag.

Now, if we talk about special relativity, it would be absurd to say that an information can travel faster than light. The effect is in synchronization with the cause in one reference frame where the effect occurs after the cause for some observer in some other reference frame.

In order to observe Newton's law of gravity all the observer's in different reference frames must observe the same phenomena which could only be possible if time were absolute and in special relativity, time is not absolute.

Therefore, Newton's law of gravity was inconsistent with the Einstein's Special Relativity.