Disrespect and disregard for sex workers is fairly common in our culture, which I think is obvious from the phrases we use to describe the practice. Saying that someone is "selling their body" or "selling themselves" is just plain wrong - a prostitute isn't even renting their body. They're using their body - and their mind - to perform a service. I dare say whatever you do for a living could probably be similarly described.
I think the anti-prostitution mindset is primarily tied to economic class, though, not necessarily the service they provide. After all, porn stars also copulate in exchange for currency, but "whore" is an insult in a way that "porn star" is not. "Whore", as a term, is closer to "hobo". Prostitution is (and, historically, has been) associated with low income, desperate straits, and crime.
So as much as Lily is misandrist, misogynist and sex negative, I don't think that's the source of her dismissive attitude towards hookers - it's simply a symptom of her preferred solution to poverty.
(If you don't mind written porn, one of the fanfics I once got was about Lily literally using a prostitute as an object. It is pretty in-character.)
As much as Lily is a weird sex-negative extremist, I do think she has a point here: "sexual frustration" isn't about glands. If it were, masturbation would be a lot more popular and actual coitus would be a lot less popular. (Other people are just such a hassle, y'know?)
And yes, I think that viewing Max's schtick as an attempt to control - or, at least, influence - people is a fair interpretation. Granted, she's trying to influence people to enjoy themselves and have orgasms, but that's still a type of control. In much the same way, I'm trying to control you to read my comics - to laugh at them, to think about them, to talk about them, etc.