I do not think it is a spoof. I have seen plenty of it appearing online in young liberal circles. Whilst this is a rather aggressive example, the general gist of it is fairly standard.
'Fat' is considered an axis of oppression like race, cis-trans, and man-woman (by identity not sex) in queer circles.
If you have the stomach for it, I'd invite you to have a peek at this publication by Cambridge University Student Union (CUSU) LGBT+, specifically the 'Significant othering' article. Choice quotes include:
Attraction down the privilege gradient: all people who identify as unattracted to a marginalised group (such as trans* people, people of colour, or fat people) have a continuing duty to challenge this part of their sexual identity
As a transsexual woman, I demand that people who ‘aren’t attracted to trans people’ challenge that self identification.
To be fair this is followed up with
This also applies to me; because transphobia can also be internalised
As a size 16-18 woman, I must challenge my received fatphobia and not to say, ‘I have a type’, when that type just happens to be the type found on the cover of socalled [sic] beauty magazines.
My point in giving that link is that it is what CUSU LGBT+ thought reasonable to publish (back in 2012) to lend some legitimacy to the idea it's not a few fringe crazies in the bowels of the internet. I have seen it frequently. Whilst not exactly mainstream, it is not uncommon in 'queer theory' circles to include 'fat' as an axis of oppression.
AspieAndProud I don't know about 'transfat' but I've seen 'fat-identified' as a thing (tried to find a CUSU source, did not manage). I suppose it's about whether you want to 'claim the identity' whatever the hell that means.
My impression is that body positivity and acceptance (you don't exist solely to be attractive to men - something I support!) somehow morphed into 'you are totally perfect and if someone isn't attracted to you they are a bigot' and somehow also 'being fat is completely uncontrollable, like your height'.
I'd definitely say that the pressure is higher on women than men - a woman adding a few pounds is treated more harshly, and instead of the health basis she is judged on her sex appeal to men, which makes it a feminist issue. However, there's a bit of a gap between that and claiming that there is not only no way for someone to control their weight but that it constitutes a queer axis of oppression...