One common theme could be the exploration of Beth Greene's character in a new light within a lesbian relationship. It might involve her coming to terms with her sexuality.
I'm not sure of specific 'Beth Greene lesbian fanfic' titles offhand. But you can try searching on fanfiction websites like Archive of Our Own. They have a large collection of fan - created stories, and you can use the search function to look for ones related to Beth Greene with a lesbian theme.
Another theme could be sacrifice. For example, Hershel might be written as being willing to sacrifice a great deal for Beth's happiness or safety, and this sacrifice is a testament to his love for her. Also, the theme of forgiveness might come up, if there are any misunderstandings or past issues between them in the fanfiction.
One place to find such fanfiction could be Archive of Our Own (AO3). Just search for 'Beth Greene and Hershel Greene' in the relationship tags, and you'll likely come across some great stories.
I hope not. Incestuous relationships are not acceptable in society and are quite disturbing. Fanfiction should also adhere to basic moral and ethical boundaries.
Definitely not. Abuse is a serious and often triggering topic. Even in the context of fanfiction, it can be very intense. It may not be appropriate for general audiences as it can cause discomfort, anxiety, or even trauma for some people who read it, especially if they have had personal experiences related to abuse.