Lampshaded: "Look, there's a girl on the other side! Fortunately, we've got one on our side, too."
Claire joins the fight for the express purpose of having a chance to rip her goody-two-shoes counterpart's face off.
Alternatively, one team recruits Alice for the sole purpose of countering any Action Girls their opponents may have.
Defied: Claire wants to fight Alice, but her male teammate's skill set is a better matchup against that particular opponent, so she lets him handle it. She fights a male opponent whom her skill set is better suited to dealing with.
Discussed: "Woo, catfight!"
Conversed: "So why is it that the female characters in action movies always fight each other?"
The Action Girl is mentally unable to fight at her full potential against men due to a tragic accident in her backstory.
Alternatively, the Action Girl doesn't fight men because she doesn't feel like it's fair to fight someone who's (technically) not allowed to fight her.
Or they do go the Les Yay / Foe Yay route but have the Claire be a Psycho Lesbian who wants to rape Alice (if she hasn't already). And even if the scene is played for Drama it both of these ladies are an example of Ms. Fanservice can invoke certain otherreactions as well. (Though to be fair there is a chance for it to be intentional especially if its a dark comedy.)
This is not a Cat Fight. This is bloody, brutal combat. There is no hair pulling, there is no torn clothing, and the only thing these girls are covered in is blood. Someone will die, and if they're lucky, they won't need to be identified by dental records (assuming they have any teeth left.) The survivor will likely leave with heavy scars at best, and possibly permanent injuries. Alice, if she survives, may be traumatized by what she just did... Or might not even bat an eyelash when asked about it later.
Reconstructed: She overcomes her mental block, but still happens to have the skills best-suited to taking down the Claire. Now, though, she can keep fighting after.