Special relativity is consistent. It just isn't completely accurate.

It's inconsistent with solid-body physics, but that's due to the oversimplifications inherent in solid-body physics, not the ones inherent in special relativity.

Trying to fit solid-body physics into general relativity is even worse. With special relativity, it works fine as long as it doesn't rotate or accelerate. Under general relativity, it can only exist on flat space-time, which basically means that nothing in the universe can have any mass whatsoever, including the object in question.