To try to answer this, let’s divide the anti-antis into three groups.
The first may not even realize that they doing this. They are not necessarily professional journalists, and they may not like Trump. But the tribal attachments to the Republican Party and the deeply ingrained distrust for the media makes it hard for them to accept the critiques on Trump as valid. We should not condemn this group too harshly because they aren’t evil, just blind. But I would ask them, please, just think how you would react to a story if it was Hillary.
The second also don’t support Trump, and may even criticize him from time to time. But they know their audience doesn’t want to hear that. The articles attacking Democrats and defending Trump get more clicks; the whataboutism tweets get the most retweets. So they balance out the occasional Trump hit with a deflection so now it’s even. They are cynically playing for the audience. They should know better.
Lastly are the Trump supporters who don’t want to admit it. It’s not respectable to be pro Trump. Anti-anti is their way of helping out while giving themselves plausible deniability when this is all over. It may be soon or it may not be for a while, but whenever Donald Trump is no longer president they want to stand up and be counted as having opposed him. I’d rather they just wear a red MAGA hat and get it over with, but they want to have it both ways.