Imagine you get an office job working as an accountant for a mining company, and one day the boss comes in and tells you that you need to go down into the mines and dig coal with the other workers. You refuse because it's not your job, and he says the it is because you tacitly agreed to do it because you didn't object on moral grounds to all the other people work do the dirty work down there so you must therefore be also willing to do it too. You'd say that was bullshit too, because it is.
They tell you what your job description is, then after you reluctantly agree to it, they change the terms of the agreement and then the main character just pretends that they're not lying when they were told that they agreed to do it in a previous conversation that never happened.
Well, one notable difference in your scenario is that I wouldn't be working at a strictly illegal operation where I would have no means of enforcing the letter of my contract beyond my own two fists. Technically, arguing with the mob is an option, but it's a very different prospect from arguing with a generic asshole boss. I mean, I'm normally a fan of unions, but Felicia and Rosalind are absolutely right that it would be a disastrous idea for the Carnations to try starting one.
There's also the issue that the contract in
PC's case is entirely verbal (unless we got more details off screen, of course). That works for and against us, but it mostly reinforces the existing power dynamic: if the two parties can't come to an agreement, who would be hurt more by walking away? As is all too often the case, the answer here is clearly the employee. The Club would have to find another gopher on the eve of the Exhibition, which isn't ideal but they have the means to do it. The MC meanwhile is back to hoping a combination of hard work and massive debt will get him through medical school, which is a much bigger gamble - to say nothing of the aforementioned risk of walking away from gangsters after agreeing to work with them.
Lastly, I still disagree that what's being asked of the MC by Kathleen is clearly beyond the scope of his job. The MC knows he's going to be working closely with whores; what the hell does he think that will involve? The Club doesn't need an employee to have sex with them on his own terms - they already have paying customers for that! What they need him for is either to keep the girls in line, or to be part of their stage shows. This
clearly falls within the purview of the latter.
So contrary to your analogy, the scenario in the game is more like a young geologist being hired by a very sketchy mining corporation to "closely supervise mining operations." When the boss (and his burly henchmen) give the MC a broken hardhat and point to the elevator, yeah, he can definitely flat out refuse, but in that case he's getting tossed out on his ass (if he's lucky). He might be able to negotiate on some details, but he *is* going to work in the mines. There is absolutely zero chance he'll get to stay in the office playing solitaire and drawing maps.
Why? What's hypocritical about it? Has he ever said that the other girls there shouldn't be allowed to refuse to do things that they never agreed to do? There's tons of jobs out there that people would never want to do in a million years, but are fine with other people doing them. If you hate the sea and can't stand the smell of fish, is it hypocritical for you to think that other people should be allowed to become fisherman if they want to?
What's hypocritical is that he's fine with the girls being ordered to strip and get fucked for money, but the instant HIS junk is mentioned he starts whining. If you're going to sell out, at least own it.
Seriously, why you guys acting like a hag handy isn't a perk of the job?
Oh, it clearly is. It's just that perks of this job are all barbed.
You seem mostly upset that Edwin decides this on his own without asking you, the player, for input. Your expectations of how "intelligent med student" should act simply evidently don't match exactly how Edwin acts, given his background, motivation and personality. But it's not really a reason to call his decision lame just because he behaves in a way you did not expect.
To play devil's advocate for a moment, part of the reason they dislike the presentation may be that we DO get a chance to refuse Kat's order, but Edwin gives an extremely lame defense: "I don't... want to."
While I agree that Kat's counterargument is decisive (namely: do your damn job!), the MC could have made a more emphatic case before backing down. That, or just removed the choice and had the MC explain his rationale internally.
IKR. People play porn games and then are like "omg, they demand me to have sex".

In all seriousness, I really hate it when sexual scenes are forced
on the player. There is, however, a big difference between forcing a scene on the player and forcing it on the main character. I can accept the latter as part of the fundamental premise of the game - at least as long as the game is consistent about it. That goes double in the early stages of a game, where we're learning how things work. But when an MC who'd previously deferred to us suddenly decides to bone some girl for no clear reason, it can definitely rankle.
That doesn't apply in this particular case since it's the prologue and there's a very clear reason why the MC is doing this, but I can understand why it would still rankle for players who can't accept that reasoning. So I do sympathize, but IMHO that just indicates the game fundamentally isn't for them. No shame in that.
Besides, Kat telling Edwin about his mother doing porn, her giving him USB drive with filth (where Darius had sex during the exhibition and I could start and finish with just that), her being dressed like she was, flirting with Edwin openly and encouraging him even to look were pretty good indicators of what he might expect when Kathleen said that "WE will interview whores". How the fuck do you interview whores? I would imagine using the tool every man has at his disposal. I don't have to be Sherlock to know that, or do I?
To be fair, the MC has no way to recognize Darius in that clip. He would recognize Killian, though, and the implications of that are rather obvious. So your point is still valid. The MC knew full well this wasn't some accounting job by the time Kathleen ordered him to unzip.