So, I have recently decided to go through RPG classics, and among those games there was Arcanum. I have decided to make a thieving/DD build, and went ahead with it, only to discover that Pettibone would not speak to me.

I have tried a lot of things: reloading the location, waiting, speaking with her in her house, using potions on my character that make her charming, levelling up just to get the Charm spell to put on her, but all she does is call me harlot and refuse to speak. Is there a way to get around it?

The only thing this quest can really affect is the thieves guild. If you want into that it's better to just do the dialogue option with the bridge thieves in shrouded hills to trick them into telling you where the guild is, then you're basically in.

That said, there's a ton of things that can influence NPC reaction.

1. Wearing nothing in your armor slot (being naked).
2. Your Beauty score.
3. Your race and gender.
4. Your reputation or alignment
5. If they saw you attack someone who isn't a monster
6. If you said something to them they didn't like.
Probably some more I'm forgetting.

Basically if an NPC's reaction value gets low enough they just will refuse dialogue. An ugly character in particular can have a lot of NPCs default to this.

This looks like it could be #2, or #5, maybe #1 but your character looks dressed.