Question

which women's right activist active made a political statement by voting illegally in the election of 1872

Answer 1

That would be Susan B. Anthony.
In 1872, she voted illegally, even though women still didn't have the right to vote. She was caught, and had to pay a fine of $100, which she never did. She wanted to make a political statement that women should be given their equal rights, which they were, many years later.