Yep. Evidence can exist that supports a hypothesis. But said evidence neither accepts nor rejects, the individual interpreting the evidence does that.
What is the opposite of evidence supporting a hypothesis? Since we are arguing semantics here. If your hypothesis is that John Smith is the murderer and you find some evidence: DNA on the murder weapon.
When DNA evidence on the murder weapon matches John Smith you would say
The evidence supports the theory that John Smith is the murderer.
What would you say when DNA evidence on the murder weapon does not belong to John Smith? Since you are arguing semantics about the word "reject"
The evidence ____________ the theory that John Smith is the murderer.
Conflicts with? opposes?
Individual: Accepts/Rejects
Evidence: Supports/Does not support
So by your logic:
I think the evidence neither supports or rejects the idea that earth is not a sphere, oblate spheroid, or spheroid.
should be changed to:
I think the evidence neither supports or does not support the idea that earth is not a sphere, oblate spheroid, or spheroid.
That really does not sound right. It's very confusing and hard to read. The evidence neither supports or does not support?
What about refute? The evidence neither supports or refutes the idea that earth is not a sphere, oblate spheroid, or spheroid.
I guess you could make your same argument based on semantics. Evidence can support a theory but not refute it. The person does the refuting.
I could also say something like there is not evidence for, or against, the idea that earth is not a sphere, oblate spheroid, or spheroid.
You could make your same argument based on semantics. Evidence can't be for or against something.
So in order to make a sentence which is easier to read I think it's perfectly acceptable, because there is no one good word which is the opposite of supporting when it comes to evidence.