One of the uses of conditionals is in situations that are <em>not real</em> or are <em>hypothetica</em>l. In this case, the normal way of using the verb to be is altered (it is used were for <em>I, he, she and it</em>) and it is followed by <em>could </em>or <em>would</em>. for example,"If I were you, I wouldn't do this."
The answer is C. Were
If the talented volleyball player <em>were</em> to accept...she could sign...today.
It would humanize her and make her capable of sympathy.
Your answer would prolly have to be D.
The answer is most likely "increased popularity" or "less negative press"