1) It is plausible that an element of affirmative action could have crept into the awarding of the Fields Medal. It is not unreasonable to suspect that it has. Any number of biases might creep in to the awarding of a prize, however major it is. For example, it could well be that a disproportionate number of Norwegians or Swedes have won the Nobel relative to their accomplishments, because of location.

2) That the mathematics of relativity (either special or general) "allows no exceptions" is trivial but as far as I can see true, because it is true of any mathematical system that exceptions to the system are, pretty much by definition, not included inside the system. Anything inside the system itself is not an exception to it. So, trivial. But not false. What we really need to to do is to see why the point is brought up.

Looking further into the matter of "exceptions", to see why he brought up the true but trivial point with respect to relativity, in the main article I found this:

The mathematics of relativity assume no exceptions, yet in the time period immediately following the origin of the universe the relativity equations could not possibly have been valid.

He appears to be saying that relativity breaks down at the Big Bang. He doesn't appear to provide any ground for making this claim, but it seems likely. Wikipedia says something similar in its article on black holes:

Theoretically, this boundary is expected to lie around the Planck mass..., where quantum effects are expected to make the theory of general relativity break down completely.

The big bang is a singularity, and in that respect is similar to black holes, so if general relativity breaks down completely in a black hole then I would imagine it would also be likely to break down completely at the Big Bang.

3) That people have often speciously used Einstein's relativity as a metaphor to promote all sorts of relativism is well known. People have similarly speciously used QM to promote all sorts of nonsense. So that particular point is hardly controversial, I think.

I have never relied on Conservapedia and don't intend to start whereas I use Wikipedia several times a day, but these particular attacks on the Conservapedia seem weak.