So I'm at a point where I'm supposed to make the demon worshippers trust me so I can infiltrate their underground lair and stuff... but as far as I can tell, the only way to increase their trust without doing either lewd stuff or evil stuff is to work as a waitress, at +1 trust each day. This will take a very long time, if that's the only way to get trust...
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It is possible to get to the Underground City on your own - you don't absolutely need the demon worshippers to trust you. Once you find the entrance it's just a matter of entering a second time with your waitress uniform to bypass unnecessary mob encounters. I mean, sure, the enemies do drop gold, but I'm pretty sure you're not nearly strong enough to make it worth your while at this point.
Though TBH going the "sneaky route" is probably meant more for a second playthrough.
What do I need to do to be eligible to learn Acedia? The wiki and the guide don't say the requirements, they just say that the demonologist teaches it, but when I go to him (after having done the demonic knowledge quiz), he just says "However, I cannot feel the negative energy required to cast a demonic spell residing within you. I'm afraid you are not compatible with demonic spells."