"How could people not see the signs that Rowling was a bigot?!"
Because the main theme in the books was that discrimination is bad.
Harry was abused by the Dursleys for not being normal in book one.
Book two showed us that wizards sometimes discriminate against people who aren't "pure blood" and against squibs.
Book three had people assuming a framed man was guilty despite minimal evidence, as well as discrimination against people with medical conditions.
Book four had an entire subplot that was removed from the films where Hagrid was being violently discriminated against for being half giant. Also, please look up what SPEW actually is. It was the name of a British women's rights organization. The SPEW subplot was supposed to be about how feminism is supposed to be about giving women a choice rather than assuming all women want the same thing. It was basically an anti-Radfem plot.
Book five was about how politicians run smear campaigns and weaponize existing prejudice to turn the public against their political opponents (the books had a lot more of this, particularly Harry being accused of mental illness by ableists to discredit him), and are willing to turn a blind eye towards horrific actions and discrimination perpetuated by government officials so long as said officials side with the government. The movies also minimized how heavily the ministry was abusing its power by removing several violent scenes of police brutality.
Book six was a look at how people can turn to extremism, whether by choice or through pressure by those around them (another story the movies ruined because they focused too much on teen drama instead of Voldemort's backstory and how he became evil.)
Book seven is a bunch of WW2 parallels. There's a reason the fandom calls the Death Eaters "Magic Nazis" and Voldemort "magic Hitler"
The Fantastic Beasts movies were in part centered around old laws banning interracial marriage (Though Rowling seemed to not understand how the US government worked, otherwise she would have known that multiple states likely would have already made marrying muggles legal by the time the series takes place since that was the IRL case with interracial marriage, and thus Queenie could have just...convinced Jacob to move away with her... instead of joining an extremist group).
Of course we're going to be shocked when the person whose entire career was built around the message "discrimination is bad and you shouldn't trust the government" starts discriminating against a group of people and defending crap the British government does.