Adele hates the term Muggle, maybe because she was once one of them.
She always sensed a dismissive attitude in the different mouths of the word.
She didn't care if those people called her a Mudblood, because in her mind, there was no difference between the word Mudblood and Muggleborn. They both represented the seemingly insurmountable gap between wizards and ordinary people.
At first she just wanted to save the people she cared about from Voldemort or Grindelwald who despised human life, but later she gradually understood their thoughts.
Adele thought that maybe she was really driven crazy by the Horcrux, and she actually wanted to overturn the secrecy law.