Someone wise once said “Men marry women thinking they WON’T change. Women marry men think they WILL change.”
The truth is, people DO change. People change on their own and people change because of the people in their life. It’s part of growing. Life doesn’t stand still. But people don’t change who they are in a basic sense. Any true, lasting relationship requires some compromise and appreciation of each other for who they are, not who you want them to be. The key is honesty, so that you know who each other really are, commitment, because there will be rough patches and disagreements, and effective communication to let the other person know where you are coming from and avoid misunderstandings (more communication is not always better, but a certain minimum is necessary).
It sounds like you are addressing the issue in a positive way, with compromise, communication and respect. As others have said: She should love who you are in a basic sense, at your core. Let her know that hunting is part of what makes you who you are, and that you’re not willing to let it go, and that, if you did, you would change who you are in a basic sense. And she doesn’t want THAT, does she? If she does, then you’re not right for each other.
Good luck with this gal (or the next one, if this one doesn't work out)!