Authors writing under pseudonyms is fine and always has been. Same as musicians, actors, comedians and performers of any 
kind. It isn’t even a terrible crime, for an author or anyone else whose work doesn’t involve physical contact or presence, to invent a persona who is very different from the living person behind the work. Well, not necessarily. Back in the 90s, for instance, most if not all male authors of erotica published their stuff under either female or femme-sounding names and no one really cared. This may have been partly because the majority of female erotica writers had pseudonyms which were elaborately glamorous as well –Valentine Diamond rather than Vicky Dobbs or whatever.
Though the biggest factor in no one bothering, or squealing ‘Catfish’ at these authors was probably that authors, particularly genre fiction authors, weren’t expected to interact with readers or even to be particularly distinguishable from one another. These days, though, it’s pretty much compulsory to share something of your actual self with potential readers via social media – and sometimes by attendance at events such as signings or conferences.
You can still do this in a way which protects your personal privacy: nearly everyone does. Pen names are fine, refusing mass-media interviews or avoiding the publication of photographs of yourself is generally respected by most people. Some writers have established enough of a reputation via their previous work that they never lack readers, so they can carry on just putting out books 
without needing to promote themselves, and they have every right to do so. It’s extremely bad form to try to out authors who have set firm boundaries simply because they believe that the only thing they owe the general public is their work.
Where it starts getting troublesome is the point where an individual is acting in what you might call bad faith, or is seeking an unfair advantage. Exhibit Unadorned has a good post on why men promoting their work under a female identity differs from women writing under male pseudonyms, and this is even more important when dealing with publishers and readers who are seeking ‘own voices’ material, whether memoir or fiction. The unbeatable poster kid for really bad behaviour in this area? This bloke. White male entitlement bingo, anyone?
But you can always rely on someone to make things worse, and quite often the someone who makes things a lot worse is going to be a cishet man. The latest outbreak of trouble lies at the door of an author who not only wrote ‘as’ a cis lesbian, using photos of (presumably or hopefully) a cis female model bought from a stock agency, but sought out correspondence from other authors, 
especially cis lesbians. You can see where this catfish is heading in catfishery, can’t you? Friendly, mutually supportive chat about writing and erotica via social media and then via private messaging, and then all of a sudden a swerve into ‘BTW my dear friend we understand each other so well so SEND N00DS!’
This isn’t on. Don’t do it. Fantasy is fine and there are more ways than ever to fulfil pretty much any fantasy you have with other consenting adults. You don’t need to get your jollies by scamming people. And no one will like you or your writing if you do
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