If that’s what you truly believe, that by consenting to a blindfold a sex worker is also consenting to sex with any one person, instead of just the person she thought she was making an agreement with, I don’t think we can carry this conversation any farther, because we have vastly different ideas about consent. Specifically, I don’t think it’s transferable.
However, I will answer your question.
When any person consents to sex, it’s based upon who they believe that person to be. If a person deliberately misrepresents an aspect of themselves, knowing that that misrepresentation would change whether the person in question would have consented, then the consent is based on a lie, and it isn’t meaningful consent.
As a fictional example: In the movie Chicago, Roxy Hart has an affair with Fred Casely, because he claims to have connections with the nightclub manager. She would not have had the affair (or, at least, not with him) otherwise. When the deception is revealed, she is so traumatized by the deception that she murders him.
Is that an appropriate response to the deception? Of course not. But it illustrates the idea that a sexual act can be traumatic retroactively, if it’s based on deception. Why? Because deception undermines consent.
The difference between your first two scenarios and your third scenario is that an off-duty cop is just a normal bloke. Deception undermines consent if, and only if, the consent was contingent upon the deception. Do I think that a sex worker would turn me away if I were an assembly line worker at a Ford plant rather than an assembly line worker at a Chrysler plant?1 Probably not, so the lie about career doesn’t undermine the consent. Do I think that she’d turn me away if I said my name was Harrison Scott instead of Scott Harrison?2 Probably not, so the lie about the name doesn’t undermine the consent.
A cop who would be arresting a sex worker would be an on-duty cop, which is a completely different thing. That’s not an omission about a career, it’s a deception about a detail so critical that if the sex worker knew that detail, the officer knows that she would not have consented. The deception therefore undermines the consent to the point where the sex wasn’t actually consensual in the first place.
1 Neither of those is my actual job.
2 Neither of those is my actual name.