"General Relativity Contradicts Itself"

The point is that you're wrong that a theory cannot contradict itself when it's mathematically self-consistent. Create a new theory by adding postulate to SR that says the speed limit is c/2. The new theory is mathematically self-consistent, yet contradicts itself (it's self-inconsistent as a whole).

Because you're wrong on that, the blog is not shown to be refuted--as you suggest--simply because it concludes that GR contradicts itself. GR could be mathematically self-consistent but still contradict itself.

The other way to tell that you are wrong is because the blog does show that GR contradicts itself, and does so simply. If the blog was wrong for any reason then it should be a simple matter to point to a statement in it and show why it's wrong. But even a supposed GR expert on another site could not do that. Every statement in the blog seems to be correct.