why is it contested and not considered?

Because the colleagues have an old view, and as a consequence, they do not accept something new. It is fairly common in the academic environment.

If the paleontologist uses orthodox evidence, why would such evidence be rejected by people who are also orthodox?

I think the word "more" in "more orthodox friends" is throwing you off. The "more" gives the impression the paleontologist is not as orthodox as his friends. Although this may be the case, you still cannot assume beyond a reasonable doubt that his more orthodox friends would shun his not so orthodox evidence. You can however assume beyond a reasonable doubt that orthodox researches will not be willing to consider the finding of someone who is not at all orthodox.

1. The part of the sentence that is related to blank (i) is this:
by his more conventional colleagues.

2. This implies that the paleontologist is less conventional. “break with” best fills the blank giving the meaning of being less conventional.

3. The part of the sentence that is related to blank (ii) is this:
“break with” orthodoxy meant that the evidence he had so painstakingly gathered would inevitably be (ii) __________ by his more conventional colleagues.

4. We see there is an antagonism in the sentence between less conventional and more conventional and hence the blank is negative in tone. Only “contested“ is correct.

5. Answer : A and E

because they're more Orthodox.