Here is the crucial point:

"Relativity theory does indeed contain inconsistencies that make it scientifically problematic. These same inconsistencies, however, make the theory ideologically powerful."

Consider an excerpt from Einstein's 1905 paper:

Albert Einstein, On the Electrodynamics of Moving Bodies, 1905: "From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by tv^2/2c^2 (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B." http://www.fourmilab.ch/etexts/einstein/specrel/www/

Is there an inconsistency in Einstein's text? At first sight, no. Einstein has advanced two postulates at the beginning of the paper and now he is drawing a "peculiar consequence" from them. Logic, that's all.

The problem is that Einstein is blatantly lying here. No such "peculiar consequence" follows from his 1905 postulates (the principle of relativity and the principle of constancy of the speed of light). Valid deduction from the postulates would have produced the following idiotic per se but correctly deduced "peculiar consequence":

From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B, as judged from the stationary system, and the clock which has remained at B lags behind the other moved from A to B, as judged from the moving system.

So if logic is obeyed, there IS an inconsistency (more precisely, idiocy) in special relativity. How does the inconsistency "make the theory ideologically powerful"? The validly deducible "peculiar consequence" is idiotic and sterile, but, without it, Einstein's 1905 "peculiar consequence", which is breathtakingly potent, would not be possible. Eventually "the clock moved from A to B lags behind the other which has remained at B" became TIME TRAVEL INTO THE FUTURE - the miracle that converted Einstein into a deity:

"The paradigm of the special relativistic upheaval of the usual concept of time is the twin paradox. Let us emphasize that this striking example of time dilation proves that time travel (towards the future) is possible. As a gedanken experiment (if we neglect practicalities such as the technology needed for reaching velocities comparable to the velocity of light, the cost of the fuel and the capacity of the traveller to sustain high accelerations), it shows that a sentient being can jump, "within a minute" (of his experienced time) arbitrarily far in the future, say sixty million years ahead, and see, and be part of, what (will) happen then on Earth. This is a clear way of realizing that the future "already exists" (as we can experience it "in a minute")." http://www.bourbaphy.fr/damourtemps.pdf