No because we know that they aren't actually doctors, and it's just a nom de plume for their artistic output. Just like Dame Edna Everage, who you mentioned, that everyone knows wasn't actually a woman but a character played by male comedian Barry Humphries.
Whereas referring to men who actually do want to be seen as women for whatever reason - such as Scarlet Blake and Isla Bryson, mentioned in the article - as women, even though they are not, is in a similar category to calling Zholia Alemi a doctor.
It is absolutely not in a similar category. You cannot compare a fraud case that prosecutors estimate cost the UK a million quid to something that costs nobody nothing.
Alemi "forged a degree certificate and a letter of verification from the University of Auckland to support her application" (quoting Wikipedia).
Transmen and transwomen are not forging any institutional credentials.
Transmen and transwomen can and do get completely legitimate, updated institutional credentials reflecting their gender.
What next, are you going to complain about someone publishing a scientific paper under her maiden name (that she's known by) rather than her legal married name? I know a couple of women who have done that.
If you meet a woman going by "Mrs." and wearing a wedding ring, then find out that she's unmarried, traveling single, and pretending to be married to keep unwanted suitors away, are you going to start calling her "Miss" and tell other people she's actually not married? Or will you be polite and refer to her as "Mrs. Smith"?
Or is Miss Smith a fraudster like the fake doctor?
The transphobes always point to the same very small number of cases as if that's meaningful. They know it's a small number, which is why they resort to using irrelevant cases like Kurtis Mawson to prop up the numbers.
The thing is, everything has a cost. Referring to people as "Dr." or "Mrs." or "Miss", or "Major", or "Hajji", or "Father", .. or changed maiden, married, divorced, and re-married names ... plus nicknames that are all context dependent. Someone might be referred to as Baron Inglewood when in the House of Lords, Mr. Richard Fletcher-Vane in the tax register, and for all I know "Stinky" to his schoolmates.
Yet we still manage to muddle through all that mismash of names, trying to be both correct and polite.
Even if you don't think it's correct for a woman to wear a wedding ring when not married, it's still polite to not let that bother you.
The small number of individual cases that highlight the flaws in the system are actually very useful. In the case of the fraudulent doctor, this caused the GMC to check all the other thousands of medical practitioners who registered under the same route, once they realised how flawed their original process had been.
Similarly, many people - including the author of the linked article - and numerous institutions are now rethinking the entire concept of pretending that males are female if they self-declare themselves as such. This is based on an increasing amount of cases where appeasing such declarations has caused significant harm or has the clear potential to do so.
For instance, the case of Isla Bryson showed how ridiculous it is to bow down to a male criminal's declaration that he is a woman and, so the ideological argument goes, must therefore be incarcerated in a woman's prison. Though, we already knew this from the Karen White case, where women prisoners were actually materially harmed with the sexual abuse he inflicted on them. These are are numerous other similar cases that demonstrate how harmful this is, and the cost to the safety and dignity of women.
Referring to any male as "she" and "her" because he requests or demands that others do so, and insists that to not do so is impolite, is the thin end of the wedge that enables all the safeguarding abuses and eradication of female-only spaces at the other end. And there's nothing at all polite about that.
Dr. Dre has a high school education and no tertiary education.
The columnist David "Doc" Searls has a bachelor and nothing higher.
Dr. Seuss didn't complete his PhD.
So what?
Sure, a few people will complain, because there's always a few people who insist we must follow The Rules.
Even if The Rules are made up.
I'm not going to refer to Dame Edna Everage as "he".
The "cost" of pronoun correctness is far less than the concrete benefits.